integrate-each-of-the-given-functions-int_13-frac4-d-x494-x2-3

Question

Integrate each of the given functions.
$$\int_{1}^{3} \frac{4 d x}{49+4 x^{2}}$$

Tyler Moulton · Accepted Answer

we want to evaluate the definite integral. The integral from 1 to 3 of 40 X over 49 plus four X square. This question is challenging our knowledge and ability to use integration methods in particular challenge our knowledge of our newfound education method and versus kinetic integral. There are two relevant integral to consider on the left. One integral d&#x27;you over route a square minus two squared equals art signed over A plus C. And on the right to integral to you over a squared plus B squared equals one over A. Are changing over A plus C. We see there are definite integral another form to So now if we identify you do you and A. We can proceed to solve that equation too. So we have U. Equals two X. Do you equal to dx on april 7? Thus are integral is of the form to with an extra multiplication factor to that we have to include in our final solution. So two times in total from 1 to 3 or two dx over 49 plus four X squared is +27 R TN two X over seven from 1 to 3 or +27 R TN +67 minus R 10 +17 as box at the bottom.

Aishwarya Krishnakumar · Answer

problem. 13 were asked to find this definite in and to do this problem, since it&#x27;s has, since it has a fraction and a function inside of the function where we&#x27;re gonna use U substitution and let you equal three X Plus two and we choose this for you because it&#x27;s a function inside of a square. So if you find the derivative of both sides, you get three d ETS. And this comes out handy because we have a three D X in our originally kitchen so we can go ahead and write this. But before doing that, we have to notice that we have bounds and in the bounds these air expounds We have changed them too. Why bound? And to do that, we just plug it into this equation who, 33 times before plus two to find the upper bound and to find the lower bound we would do three times one plus two. So the upper round is 14 and the lower bound is five. And now we can do the U substitution so would be won over you squared times the u. So this equals you to the minus one over. Now get a one. And you would evaluate this from I to 14. So that just means you have to plug in 14 in replacement of you and then minus Have to plug in five in replacement of you. And this gives us one over 14 minus one word. Negative five. Is this nine over 70?

Aishwarya Krishnakumar · Answer

for problem 19 were out to u substitution to find this indefinite integral. So we&#x27;re gonna let you equal the denominator. U equals X to the four plus for X squared plus seven. Now we take the derivative of both sides, maybe four x cubed eight. Thanks D x, and you can simplify this by taking out a two X. Actually, you could take it a four x my bad B X squared close to detox and then you can divide both sides by four. It would be do you over four equals x times X squared clothes two times d x So now as you can see this, if you foil it, this would be right a year x cubed plus two x, which is the same thing as a the numerator of the original equation. So that makes it easy when we rewrite this interval. So it beat the integral of won over you because of this. And instead of the three X, we would have do you over four and you can move the constant the front would be won over four, which was the constant and then the integral of you to the negative first power and in a girl of one of her you is out and of the absolute value off you. And don&#x27;t forget the plus C, and you cannot have a you in the answer. So we&#x27;re gonna plug in this You So, Helen, uh, next to the floor waas four x squared plus seven post C and this is the answer.

Amy Jiang · Answer

Okay, so let&#x27;s start another thing that we have a fixed in power for here, and then we&#x27;ll go toe that we get extra party, which is what we have in our numerator. So what do we let you equal our denominator? Okay, I know. Let&#x27;s take our derivative or hit, and then we get the nuts. Okay, so we have an X cubed plus two X. So we confront their out of four here. And that leaves us exactly what with what we once so would you divide by four on both sites? Okay, I know it&#x27;s here. That&#x27;s gonna be RG you or do you over four in this portion here, that&#x27;s are you. So we get the integral of do you over four and in you. So it&#x27;s factor out a woman. Okay, so we get 1/4 in a little of do you over you and are integral. That&#x27;s you. Cool, too. That&#x27;s critical to Ellen of you. I see. To be an Ellen of you, that&#x27;s extra part four parts for X squared plus seven and in policy

Amy Jiang · Answer

because what start very letting you equal to X. Because three and I always take the derivative of that. So that gives us, um, Do you eat a culture too? The X So it was here that we have before she lets break that up into two times two. So we bring out one of the twos and have a two inside. So we see that, um and Bill, we have to the ex unethical to do you and then this inside two X Plus three. That&#x27;s equal to you. So we&#x27;re placing our extra for used. We get the following we get you to the power of four times to you and then we can take the Serono. So that&#x27;s two times you two par five over five plus See another. Let&#x27;s put back in or you Are you is two x plus three and that&#x27;s did a part of five over five plus C

Xiaomeng Zhang · Answer

So we&#x27;re used a substitution here. So two times this is sakes for one over to ax minus seven. The power of to And then we can this access to and them and seven because the relative off the term just dress each house. Who because of the rotor off the stern, dressy coaster tool sewing into time? Ah, hop here. And also we need to change the range time Tumen seven comes to my seven. See? That&#x27;s what you comes. Who? 51 so long over it. You, Squire. You. So that s one e count too. I want you could power off miners to you. Well, how? My notes U to the power off miners. One by one, we kill to my nose. 13 Smart man knows one Reach Eco&#x27;s who floor over

Problem

Integrate each of the given functions. $$\int_{0}…

Problem 10 Easy Difficulty

Integrate each of the given functions.
$$\int_{1}^{3} \frac{4 d x}{49+4 x^{2}}$$

Answer

$\approx 0.1229$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$\approx 0.1229$

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Kayleah T.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Kayleah T.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus