integrate-each-of-the-given-functions-int_0ln-2-x-ex-d-x-2

Question

Integrate each of the given functions.
$$\int_{0}^{\ln 2} x e^{x} d x$$

Vikash Ranjan · Accepted Answer

In the problem we have integration 02, two. Excuse the bar X D X. So this is equal to X for x minus integration one into your Barracks DX. So this is written as X products -8. Bar x. We are pushing the limits of zero and Ln two. Therefore it is L N to the power Ln two minus eight power Ln two minus zero power zero minus eight power zero. Therefore it is Ln two into 2 -2- of -1. This is twice Ln two minus two plus one, which is equal to Twice Ln 2 -1. And this is the answer.

Amy Jiang · Answer

I guess they were asked to find the integral of the fallen. We don&#x27;t have this integral in our table, but we continue like this in terms of hyperbolic sign and co sign. So let&#x27;s do that. So we get the four way and if you&#x27;re use ah you sub, we can let you be equal to Coche of X. And we know that the derivative of coach that lets you put the finish of that&#x27;s the guts. And now let&#x27;s replace our, um, are you values to? So at X is equal to a one or two we have u is equal to coach appellate into, and that&#x27;s equal to 1.25 And then when X is equal to zero, we have that use equal to push zero, and that&#x27;s equal to one. Okay, so we&#x27;ll slip fill in our employ its and change this in turns off you. So we have from now 1 to 1.25 of one over you. Do you that use me, Ellen of the absolute value of you have all waited at 1.25 And what So we get Ellen of 1.25 minus old and a one which is oh, so we just get this is our answer

Amy Jiang · Answer

Okay, So looking at their on a 6.4 and we have in a grove of tangents of heart trouble extensions, So that&#x27;s that&#x27;s equal to natural log. Uh, however, ball co sign of our term inside with his ex. And I were Valerie that Eleanor too, And, um girl. So that gives us natural log of kohsh uh, the natural log of to and in minus the natural log of Kohsh of Zero, Coach of Zero. What&#x27;s seeing Coach Zeros equips one. So we have Ellen of one, which is equal to zero. So this is equal to the natural log of I bought co sign of the natural log of to

Amy Jiang · Answer

Okay. So, looking at their own six point on, we have the inner girl of I provide close begins, not equal to the natural laws of that value of hyperbolic tangent of X over two. And this is it all the way to add our endpoint. Okay, so that gives us the natural laws of tangents. Uh, the natural laws of degree over to I didn&#x27;t minus the natural log of absolutely attentions. Uh, the natural log of to over to Okay, so this is our solution.

Ramzi Deek · Answer

so integral from zero to l enough to of X E to the X dx. So you is equal to X Do you is equal to one. So I&#x27;m gonna take this as you and D V is e to the X So will the integral feet of the X will just be you to the X. All right, so moving on from there is an integral A few devi is u V minus integral of v Do you? So you ve is X E to the X minus integral of V d u That&#x27;s e to the X as well. So our answer is X e to the X minus e to the X So we need to integrate this from zero to Ellen to All right, So let&#x27;s start with Ln two he to the l n two minus c to the l N two minus zero e 20 minus you to the zero. Remember when you raised to a power of zero, have it becomes one, so l enough to I&#x27;m just going to keep it as Ln of to e to the l enough to is the same as, uh, it&#x27;s too basically. So this becomes to Ln two minus two, minus two. Here, this is zero E to the zero is one minus. Negative thoughts plus one here. So our final answers to Ln two minus one.

Alex Johnson · Answer

this problem were going to calculate the anti derivative of E to the X co C can&#x27;t be g X co tangent to be DDX and our first step is toe select a use substitution value which will be e to the X that gives us d&#x27;you, which is either the x d x and so to change are integral into values of you. We get cosi can&#x27;t of you multiply by cho tangent of you d you an anti derivative will be negative. Cosi can&#x27;t of you plus C and will change this back into terms of X.

Problem

Integrate each of the given functions. $$\int x \…

Problem 21 Easy Difficulty

Integrate each of the given functions.
$$\int_{0}^{\ln 2} x e^{x} d x$$

Answer

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Kayleah T.

Samuel H.

Michael J.

Joseph L.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 28

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Kayleah T.

Samuel H.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Basic Technical Mathematics with Calculus

Kayleah T.

Samuel H.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Kayleah T.

Samuel H.

Michael J.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus