integrate-each-of-the-given-functions-int_14-fracesqrtx2-sqrtx-d-x-3

Question

Integrate each of the given functions.
$$\int_{1}^{4} \frac{e^{\sqrt{x}}}{2 \sqrt{x}} d x$$

Tyler Moulton · Accepted Answer

we want to integrate the following expression. The integral from 1 to 4 of each of the square root of X divided by two root X. D. S. This question is testing our knowledge of methods of integration in particular. It&#x27;s testing our ability to deploy such methods as exponential integration. Remember that exponential integration states that the integral of either the U. D. U. Is either the U. Class C. So if we identify you do you and our problem we can go ahead and solve using this formula since you is whatever is raised to the power of E and are integral. It must be that you as root X. Which means to you is 1/2 X. Dx. Thus we see they are integral perfectly matches integral to the U. D. U. Which means we can plug in either the U plus see from our bounce so interview interview do you is even the X. From 1 to 4, plugging in one and four. Let&#x27;s evaluate this definite integral as e squared minus heat.

Amy Jiang · Answer

Okay, so we have the fallen. And also let&#x27;s rewrite this term and at the term off power to looking at this as extra part of to the power of to. And now let&#x27;s let you be equal to extend Part two and into you, as you put it to X, the X So that gives us this. Is it people to you over two x squared in a girl off one plus use word and I&#x27;ll note that this export here, deaf people to you. So let&#x27;s replace that. And now this is equal to negative 1/2 are symbolical sequins, inverse of absolute value of you and then plus C replenishing. Are you with X X? Where did we get the following?

Matt Just · Answer

right. So you have a definite integral here in a girl. Negatives for toe one of square it of two t x. So, by the fundamental theorem of calculus, we just need to find an anti derivative of root tubes that would just be rude, too x and then evaluated from negative or the one. So that&#x27;s just gonna be rude. Tio times one minus ninety four, which is five twenty.

Xiaomeng Zhang · Answer

so bad a Ruoff integral we know thus one dressing counts to square roots, off to terms axe And here is a one and minus full. And the mix of procured those acts here that is both grassroots off to my nose Miners school times of square roots off to so that echoes who five comes from square root.

Amy Jiang · Answer

Okay, so no zero that we have a square root of X inside our hyperbolic seek it and then we have one over the square root of so we can use Yusoff. Well, you&#x27;ve equal to the square root of X and then we have to you. That&#x27;s equal to 1/2 except of native 1/2. Yes, on well, with me, I that as one over it&#x27;s where of X Times two. Now let&#x27;s wanted part two on both sides. So we get to do you is equal to one over the square root of X the X this portion right here that&#x27;s to do you and then we have this portion inside here. But people to you know, let&#x27;s replace or endpoints or find are you and points. So at, um, X is equal to four. We have use equal to the square root of four and that&#x27;s it. Til on at X is equal to zero. R u is equal to tell. Okay, so we have the integral from 0 to 2 of sequence or sorry, Harper. Folic sequins squared of you to do you and we have another interval. Curtis, this is equal to, um it&#x27;s seeing hyperbolic seeking square is tangents Archibald tensions of you and then evaluated at two and girl to that too. Hyperbolic tensions of two minus to hyperbolic tangents. Zero. And this portion is equal to zero who got to hyper ball attendants to?

Amy Jiang · Answer

against sinners that we have a square root of X on the square root of X here. So why don&#x27;t we set you to be equal to the square root of X? And then we know that, do you? That&#x27;s equal to 1/2 Burgert of X dx. Now we don&#x27;t have a 1/2 year, so we multiply bites you on both sides. So we have to do to you is equal to the fallen. Okay, so what&#x27;s your place? What we have we now have, um it&#x27;s already should be actually a to number four. So we have hyper box Deakins squared of you and then we have to do you and our endpoints. Well, it is. If X is equal to four, the new is equal to two of x physical digital you is equal to zero. So we are from 0 to 2. Okay, so the integral of hyperbolic seeking squared. That&#x27;s this hyperbolic tangent of you and I will have always this at to Andrew. Okay, So hyperbolic. Um tangents. Zero. That&#x27;s zero. So we actually got to hyperbolic tangents. I&#x27;m to

Problem

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

Problem 11 Easy Difficulty

Integrate each of the given functions.
$$\int_{1}^{4} \frac{e^{\sqrt{x}}}{2 \sqrt{x}} d x$$

Answer

$e^{2}-e$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$e^{2}-e$

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Catherine R.

Kayleah T.

Caleb E.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus