Let f be a differentiable function such that f(0) = 5. 420 and f'(x) = sqrt(sin²x+x). What is the value of f(2pi)?

Answers

Answer 1
General Formulas and ConceptsCalculus

Differentiation

DerivativesDerivative Notation

Integration

IntegralsIntegration Techniques

Integration Rule [Fundamental Theorem of Calculus 2]:
[tex]\displaystyle \frac{d}{dx}[\int\limits^x_a {f(t)} \, dt] = f(x)[/tex]

ApplicationStep 1: Define

Let's organize what is given to us from the problem.

We are given an initial condition: f(0) = 5.420

We are given a derivative:
[tex]\displaystyle f'(x) = \sqrt{\sin^2 x + x}[/tex]

We are asked to find f(2π).

Step 2: Work

We can first formulate a rough function using integration rules, namely the Fundamental Theorem of Calculus (2nd part):

[tex]\displaystyle f(x) = \int \limits^{x}_{a} f(t) \, dt + C_0[/tex]

where f(t) is a derivative function and C₀ is an initial condition.

Now that we have a "baseline formula", we can substitute in our f(t) derivative function, our limits, and our initial condition:

[tex]\displaystyle f'(x) = \sqrt{\sin^2 x + x} \Rightarrow f(t) = \sqrt{\sin^2 t + t}[/tex]

[tex]\displaystyle \begin{aligned}f(x) & = \int \limits^{x}_{a} f(t) \, dt + C_0 \\& = \int \limits^{x}_{0} \sqrt{\sin^2 t + t} \, dt + f(0) \\& = \boxed{ \int \limits^{x}_{0} \sqrt{\sin^2 t + t} \, dt + 5.420 } \\\end{aligned}[/tex]

∴ our general function is equal to:
[tex]\displaystyle \boxed{ f(x) = \int \limits^{x}_{0} \sqrt{\sin^2 t + t} \, dt + 5.420 }[/tex]

*Note:

There isn't an antiderivative for the general function, so you will have to input the integral into a calculator.

In order to find the value of f at , we substitute x = 2π into our general function:

[tex]\displaystyle \begin{aligned}f(2 \pi) & = \int \limits^{2 \pi}_{0} \sqrt{\sin^2 t + t} \, dt + 5.420 \\& = 11.44863485704886 + 5.420 \\& = 16.868634857 \\& \approx \boxed{ 16.868 } \\\end{aligned}[/tex]

∴  [tex]\displaystyle \boxed{ f(2 \pi) \approx 16.868 }[/tex]

Answer

∴ the value of f(2π) is approximately 16.868.

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Topic: Calculus I

Unit: Integration


Related Questions

Uan inveted $5000 and bill inveted $1500. Why did uan have a higher balance at the age of 65

Answers

Uan had a higher balance at the age of 65 because he invested higher amount that Bill who invested $1500 and Uan receive way more according to compound interest.

What is compound interest?

Compound interest is calculated by multiplying the initial principal amount by one and adding the annual interest rate multiplied by the number of compound periods minus one. The loan's total initial amount is then deducted from the resulting value.

Compound interest is interest calculated on the initial principal, which includes all previous periods' accumulated interest. The ability to generate "interest on interest" is referred to as compound interest. Interest can be compounded at any time, from continuous to daily to annually. Money is multiplied at a faster rate when compounded.

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WILL MARK BRAINLIEST PLEASE HELP URGENT
In a banking system with limited reserves, which of the following combinations of monetary policy is the most expansionary? (1 point)
(I think the answer is c)

The central bank's selling bonds and lowering the discount rate

The central bank's buying bonds and Congress increasing government spending

Congress lowering taxes and increasing government spending

The central bank's lowering the required reserve ratio and lowering the discount rate

The central bank buying bonds and increasing the required reserve ratio

Answers

Answer:

c

Explanation:

congress lowering taxes and increasing government spending

calculate how much more energy a magnitude-9 earthquake releases compared to that of a magnitude-7 earthquake

Answers

Answer:

16.1 earthquake

Explanation:

hope it helps

Living in urban environments can influence an individual's behavior.
Please select the best answer from the choices provided
ОТ
OF

Answers

Answer:

True.

Explanation:

Sociology can be defined as a social science that deals with the study of the socio-cultural interaction of humans with respect to the structure, functioning and development of their society.

The main purpose of sociology is to develop and enhance human knowledge or understanding of important socio-cultural processes through the gathering and analysis of all aspects of the social life of the people living in a society.

A sociologist refers to an individual (scientist) that studies sociology i.e a social scientist.

Generally, sociologists study how society affects a group of people and how the people affect the society in return.

Living in urban environments can influence an individual's behavior because an environment is a determinant factor of how a person behaves and act.

For example, a person living in an urban environment is more likely to use a global positioning system (GPS) or digital map to find direction in moving from one location to another.

Answer:

True

Explanation:

Hope this helps

HELPPPPP PLEASEE WILL mark brainliest

Answers

Answer:

Explanation:

The CORRECT answer is C as the birth weight distribution and hence its histogram should be symmetrical from its mean value.

Answer:

Explanation:

ans is c as distribution should be the same left n right of the mean

What is good for one might not good for others?

Answers

Answer:

[tex]\huge\colorbox{violet}{✏﹏ \: ᴀɴsᴡᴇʀ \: }[/tex]

Well, you can take the example of different genres of music. One person might like pop while others might be more interested in country, jazz, hip hop etc. So, what seems good for one might not seem good for others due to their tastes in different things.

[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]

Long time no see brainly well I asking do VLONE shirt on Amazon are they legit like is it real

Answers

lol haha probably not. Nothing on Amazon is real

Which of the following careers is the most highly resistant to economic change?


Computer Technician

Barber/ Hairstylist

Machine Designer

Photographer

Answers

Answer:

Barber/ Hairstylist

Explanation:

For each of the following pairs of terms, explain how the first concept influences the process indicated by the second. Be sure to define the first term and then apply it to the second.



Rods, Peripheral Vision Motion Parallax, Depth Perception Proximity, Perception McGurk Effect, Audition

Answers

The explanation of  how the concept influences the process indicated are given below

What are the concept?

Rods are light-sensitive cells found in the retina of the eye that are responsible for detecting low levels of light, such as in dim or dark conditions. They are more sensitive to light than the cone cells, which are responsible for detecting color and finer detail. Rods play a role in peripheral vision, which is the ability to see objects or movement that are outside of the center of the visual field.

Motion parallax is the phenomenon in which objects that are closer to us appear to move faster than objects that are farther away when we move our head or eyes. Depth perception, the ability to perceive the distance of objects in three-dimensional space, is influenced by motion parallax because it provides us with information about the relative distance of objects. When we move our head or eyes, the movement of nearby objects is more noticeable compared to distant objects, which helps us determine their relative distance.

Proximity is the physical closeness of objects or elements. Perception, the process of interpreting and organizing sensory information in order to understand the environment, is influenced by proximity because it can affect how we group and organize visual information. When objects or elements are close together, we are more likely to perceive them as being related or belonging to the same group, whereas when they are farther apart, we may perceive them as being separate or unrelated.

Therefore, The McGurk effect is a phenomenon in which the sound of a spoken syllable is altered or changed by the visual information of a speaker's mouth movements. Audition, the process of hearing

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Which costs more...trade school or college?

Answers

Answer:

College

Explanation:

College costs about $9,410 per year, while trade schools cost anywhere from $5,000 - $15,000 total.

Based on the data in the map and your knowledge of world history, the global community's reaction to the spread of the Ebola virus was similar to which of the following historical examples?

The United States' response to the AIDS epidemic in the late 20th century

The response to mass deaths throughout Europe due to the black plague in the 14th century

The reaction of American Indians to massive outbreaks of smallpox in the late 15th century

The reaction of the Chinese government to the proliferation of opium addiction in the 19th century

Answers

Answer:

by my re search it's C

Explanation:

Based on the data on the map, a similar reaction from the global community was B. The response to mass deaths throughout Europe due to the black plague in the 14th century

What is the Black Plague?

This refers to a period in history when there was a severe outbreak of disease and plague in Europe that took the lives of many.

Hence, we can see that based on the reaction to the Ebola virus in the global community where people were transferred and quarantined and stringent measures were put in place, this is similar to the response to mass deaths throughout Europe due to the black plague in the 14th century.

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In relation to the video “What Most Schools Don’t Teach,” the authors mention Jane Margolis’ “unease” (paragraph 3, sentence 1) primarily to
A. provide supporting evidence for the video’s claims about the importance of perseverance in learning to code

B. demonstrate that the video creates false expectations regarding the financial rewards of careers in computer science

C. rebut the video’s premise about the steps required to make programming skills more widespread

D. suggest a more effective way to make programming seem appealing to those outside the computer science community

E. acknowledge more fully the achievements of women in the computer science community

Answers

Answer:

C. rebut the video’s premise about the steps required to make programming skills more widespread

Explanation:

Answer C

Correct. According to the passage, Margolis feels “unease” because the video fails to acknowledge that not everyone has access to certain “fundamental factors” required to learn programming. By bringing up Margolis’ unease, the authors rebut the video’s implicit assumption that making coding seem more desirable (for example, by portraying it as fun or lucrative) is an effective step for increasing the number of people who actually do learn to code.

Answer:

C

Explanation:


Tilda took a random sample of n = 17 redwood trees in a park she oversees and had their heights
measured. The heights were roughly symmetric with a mean of = 60 meters and a standard deviation of
Sy = 6.1 meters. She wants to use this data to construct a t interval for the mean height of all the
redwood trees in her park with 95% confidence.
Con
What critical value t' should Tilda use?

Answers

Answer: t* = 2.120

Explanation:

Answer:

t*=2.120 is correct

Can you figure out the next
three digits in the pattern
33633456??

Answers

Answer:

912

Explanation:


I need this to graduate!!


PLEASE HELP ASAP!!!

Viewing guide. We are going to watch the 1995 movie of Othello looking for the references to the scarf, listening for references to monsters, demons, and hell, and paying close attention to Iagos’s words to see how each of these was used to develop the theme of the danger of jealousy in the play.

Essential Question: How does Shakespeare develop a theme of the danger of jealousy in the play Othello?

Iago’s words
How do they connect to the theme of jealousy?

Example:

Explain:


Example:

Explain:


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Example:

Explain:




Scarf: What does it symbolize? How is it used to develop the theme of jealousy?

Example:

Explain:


Example:

Explain:


Example:

Explain:




Hell, demon, and monsters: References to hell, demon, and monsters are repeated as a motif. How do they connect to the theme of jealousy?

Example:

Explain:


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Explain:


Answers

Answer:

Explanation:

Ted might eat the cake.

Was Flaubert’s an accurate portrayal of bourgeois marriage in this description of Emma and Charles?

Answers

Answer:

Explanation:

In Gustave Flaubert's novel "Madame Bovary," the characters Emma and Charles Bovary represent a portrayal of a bourgeois (or middle-class) marriage in 19th-century France. The novel, which was published in 1857, portrays a story of Emma who, feeling trapped in her mundane and unfulfilling married life with Charles, seeks fulfillment through extramarital affairs and extravagant spending.

Flaubert's portrayal of Emma and Charles' marriage is one of dissatisfaction and unhappiness. Charles, a well-meaning but dull and unexciting man, is unable to provide Emma with the emotional and intellectual stimulation she craves. Emma, meanwhile, is restless and yearning for a more exciting life, which leads her to engage in extramarital affairs and overspending.

Flaubert's portrayal of Emma and Charles' marriage is generally seen as an accurate portrayal of the bourgeoisie marriage of that time, as it highlights the societal expectation placed on women in particular to conform to a traditional and domestic role in marriage, and the limited opportunities for personal and intellectual growth for both partners. Furthermore, the novel also illustrates the financial struggles faced by the Bovarys and the moral judgment imposed on Emma as a woman who goes against societal expectations.

It's important to remember that "Madame Bovary" is a work of fiction and therefore it may not be entirely accurate, but it is considered to be a representation of that time's society and the reality that many individuals faced in those conditions.

In what ways is the film, The Princess and the Frog, important/relevant to our everyday life and society?

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It’s the frog you really just got to read it right that’s all

In Stand and Deliver, what are you impressions of the town? What feelings do you get about the neighborhood? Which ethnicity is in this neighborhood, and what makes this known?

Answers

In the movie stand and deliver the impressions of the neighborhood could be in between middle and lower class people, the neighborhoods could also be violent, the most popular ethnicities in that neighborhood are Chicanos you can tell by watching the movie

Identify the rhetorical device Wiesel employs in paragraph 1-2. Why does he include it?

Passage: “Hope, Despair, and Memory” By Elie Wiesel

Answers

Wiesel uses ethos, logos, pathos, heated language, and other rhetorical strategies to evoke compassion in his lecture, which is a scathing criticism of people who choose to ignore the pain of others.

What rhetorical strategies does Elie Wiesel employ?

Elie Wiesel emphasizes and establishes the issue of losing faith by using rhetorical tactics like personification, analogies, and rhetorical questions. Elie Wiesel used personification as one of his rhetorical strategies to develop and accentuate the issue of losing faith.

What kind of imagery does Wiesel utilize in paragraph 20 and what effect does it have? 

Wiesel compares what occurred to the Jewish people to "a tidal surge of hatred" (par. 20). The reader might picture the Jewish people being engulfed by a great flood of hatred.

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Which of the following statements illustrates the impact of the reform era (1900–1920) on US political parties?


A) Reforms strengthened the ability of political parties to hold officeholders accountable.

B) Reforms limited the power of political parties by reducing the number of government positions they controlled.

C) Reforms led parties to reduce the influence of party bosses by using nominating conventions to choose their candidates.

D) Reforms led political parties to reduce voter requirements, making it easier for people to participate in elections.

Answers

Answer:

The correct answer is C. Reforms led parties to reduce the influence of party bosses by using nominating conventions to choose their candidates.

Explanation:

The Reform Era was a period of American history, from the 1900s to the 1920s, during which the nation's political system underwent a radical change, through which the political corporatism prevailing until then was abandoned, to move to a more democratic and transparent. Until then, and mainly at the local level, political machines dominated the nomination of candidates based on nepotism, favoritism or political favors. After the reform, candidate selection systems were created, or they were massified (as in the case of political conventions), thus taking power away from political machines and democratizing the system for selecting public officials.

Answer:

c

Explanation:

calculate how much more energy a magnitude-9 earthquake releases compared to that of a magnitude-7 earthquake

Answers

Answer:

To calculate how much more energy a magnitude-9 earthquake releases compared to that of a magnitude-7 earthquake, you can use the formula:

Energy (magnitude 9) = Energy (magnitude 7) * (10^(3/2))^(9-7)

Plugging in the values, you get:

Energy (magnitude 9) = Energy (magnitude 7) * (10^(3/2))^(9-7)

= Energy (magnitude 7) * (10^(3/2))^2

= Energy (magnitude 7) * 10^3

= Energy (magnitude 7) * 1000

This means that a magnitude-9 earthquake releases 1000 times more energy than a magnitude-7 earthquake.

What’s the line of reasoning in the article “Gender pay gap will remain until companies change their ways (opinion) CNN Business by Natasha Lamb and Jennifer Klein

Answers

for that you need to increase your basic competition

WILL GIVE BRAINIEST IF CORRECT!!!!!! AND EXTRA POINTS!!!
Alex can stack exactly 16 cookies with a diameter of 5 cm in a cylindrical container of volume 100.- em.
What is the thickness of each cookie?

Answers

Each cookie is about 5cm

I need this answered right away, please!!
In which material will sound waves travel faster?
A.air
B.rock
C.vacuum
D.water

Answers

Answer:

rock

Explanation:

this is because rock is a solid , sound travel faster in solids

PLEASE ANSWER THIS ASAP I WILL MARK YOU THE BRAINLIEST THIS IS A SCIENCE QUESTION
Fusion reactions in the sun change nuclear energy into
mechanical energy
chemical energy
electromagnetic energy
potential energy

Answers

Answer:

electromagnetic energy

The chart above compares credit card offers. What is the most significant drawback to Credit Card 1 relative to the other cards? (1 point)

Higher interest rate
Low limit
No rewards
Secured credit

Answers

Answer:

the most significant drawback to Credit Card 1 relative to the other cards is that it has a higher interest rate. The interest rate for Credit Card 1 is 15.99%, which is higher than the interest rates for Credit Card 2 (12.99%), Credit Card 3 (13.99%), and Credit Card 4 (14.99%). This means that Credit Card 1 will be more expensive to use than the other cards, as the interest charges will be higher. This is a significant drawback, as it will increase the overall cost of using the credit card.

Explanation:

PLEASE HELP!!!! I need sources and arguments for this prompt. Please cite your sources
Write an essay in which you come to a definitive conclusion about how members of Congress decide to vote. Support your conclusion with information from The Lanahan Readings excerpts listed on the assignment page, as well as outside research.
As you research and formulate your response, ask yourself these questions:
Are members of Congress "single-minded seekers of re-election," as Mayhew claims?
How does the "home style" of members relate to their decision making in Washington, D.C.?
How can we best define "pork"? Is dishing out the pork a recipe for electoral success, and if so, how does it influence congressional behavior?
Is the threat of legislative gridlock a necessary evil to force members of Congress to compromise?
How do the decisions of members of Congress change when the government is divided? What about during the "lame duck" portion of a president's term?
Which theoretical role — delegate, trustee, or politico — best describes most members of Congress when they make decisions?

Answers

Answer:

Members of Congress are often thought to be "single-minded seekers of re-election," as suggested by Mayhew. This theory suggests that members of Congress are primarily concerned with their own political survival and will prioritize their own re-election over the needs of their constituents or the greater good of the country.

There is some evidence to support this theory. For example, research has shown that members of Congress tend to focus their efforts on constituent services and pork barrel projects, which are designed to bring tangible benefits to their districts, in order to improve their chances of re-election. These efforts can sometimes come at the expense of more significant policy decisions or broader national interests.

However, it is important to note that members of Congress also have other factors that influence their decision-making. For example, the "home style" of a member, or the way in which they interact with their constituents and engage with their local community, can also play a role in their decision-making. Members who have a more collaborative and consultative home style may be more inclined to consider the views of their constituents when making decisions, while those with a more directive home style may be more likely to prioritize their own views and beliefs.

Pork barrel projects, or narrowly targeted spending initiatives that are designed to benefit a specific district or group, are also a significant factor in congressional decision-making. While dishing out pork can be a recipe for electoral success, as it brings tangible benefits to a member's district, it can also contribute to legislative gridlock if members are unwilling to compromise on their own pork projects in order to pass broader legislation.

The threat of legislative gridlock can sometimes be a necessary evil to force members of Congress to compromise and find common ground. However, it can also lead to inaction and a lack of progress on important issues.

The decisions of members of Congress may also be influenced by the overall political climate, such as whether the government is divided or whether the president is in the "lame duck" portion of their term. During times of divided government, members may be more likely to prioritize their party's goals and ideologies over finding common ground with the opposition. Similarly, during the "lame duck" period, members may be more likely to take bolder, less politically risky positions as they are no longer facing the prospect of re-election.

In terms of theoretical roles, it is likely that most members of Congress exhibit a combination of the delegate, trustee, and politico roles when making decisions. Delegates are primarily concerned with representing the views of their constituents, trustees prioritize their own judgment and expertise, and politicos are primarily motivated by political considerations and the pursuit of re-election. The specific balance of these roles may vary from member to member and may also shift depending on the specific circumstances and context of the decision at hand.

Overall, it is clear that there are a number of factors that influence the decision-making of members of Congress, including the pursuit of re-election, the "home style" of the member, pork barrel projects, the threat of legislative gridlock, the political climate, and the individual member's theoretical role.

(iii) Describe a reasonable research method that the ecologists could use in their
physical control efforts. *

Answers

Answer:

Researchers can use the research method known as modeling.

Explanation:

To research the possibility of physical control in ecology, the best research method that researchers can use is the method called modeling. This is because modeling allows the creation of an ecosystem model, which represents the entire ecosystem in a reduced size, presenting all elements of the real ecosystem. This model allows the researcher to apply methods of physical control that would not be possible to be applied and analyzed in the real world. The model allows the researcher to analyze the entire composition of the physical control and all the results that they can cause, reaching efficient conclusions.

PLEASE HELP!!!! If you do this correctly, I will mark you as brainliest. I've tried a few times and no one seems to do this correctly. I need sources and argument points that work this.
Write an essay in which you come to a definitive conclusion about how members of Congress decide to vote. Support your conclusion with information from The Lanahan Readings excerpts listed on the assignment page, as well as outside research.
As you research and formulate your response, ask yourself these questions:
Are members of Congress "single-minded seekers of re-election," as Mayhew claims?
How does the "home style" of members relate to their decision making in Washington, D.C.?
How can we best define "pork"? Is dishing out the pork a recipe for electoral success, and if so, how does it influence congressional behavior?
Is the threat of legislative gridlock a necessary evil to force members of Congress to compromise?
How do the decisions of members of Congress change when the government is divided? What about during the "lame duck" portion of a president's term?
Which theoretical role — delegate, trustee, or politico — best describes most members of Congress when they make decisions?

Answers

Answer:

Members of Congress are elected officials who are responsible for representing the interests of their constituents and making decisions on behalf of the country. According to Mayhew, they are "single-minded seekers of re-election," meaning that their primary goal is to get re-elected and they will do whatever it takes to achieve this goal. This can include dishing out "pork," or funding for projects in their districts that are not necessarily related to the larger issues facing the country. These projects are meant to gain the favor of constituents and increase the likelihood of re-election.

The "home style" of members of Congress also plays a role in their decision making. This refers to the values and beliefs of the individuals and how they reflect the culture and politics of their districts. Members of Congress may feel pressure to align with the views of their constituents and may prioritize their needs and desires over the needs of the country as a whole.

During times of divided government, the decisions of members of Congress may change as they are forced to compromise with the opposing party in order to pass legislation. This threat of legislative gridlock can be a necessary evil to force members to come to an agreement and avoid complete stagnation.

In terms of their theoretical roles, most members of Congress can be classified as "politicos," meaning that they prioritize their own political careers and interests over their role as a representative. However, some may act as "delegates," strictly following the wishes of their constituents, while others may take on the role of a "trustee," using their own judgement to make decisions for the good of the country.

In conclusion, the decision making process of members of Congress is complex and influenced by a variety of factors, including their desire for re-election, the values and beliefs of their districts, and the political climate. While some may prioritize the needs of their constituents and act as delegates, others may prioritize their own political careers and act as politicos. The threat of legislative gridlock can also play a role in their decision making, as it forces them to compromise and find common ground.

According to the memorandum, which of the following best explains the root of the tensions between the Soviet Union and the United States?

The building of the Berlin Wall to divide the former German capital into West and East occupation zones
The successful launch of Sputnik I, the first successful artificial satellite, by the Soviet Union
The inherent conflict between capitalist and communist economic policies, markets, and trade
The Soviet fear of world conflicts due to interference from the United States in communist nations

Answers

In my opinion it’s not the root but of your options the last one makes the most sense.
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