Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Evaluate the integral using integration by parts with the indicated choices of $ u $ and $ dv $.

$ \displaystyle \int xe^{2x} $ ; $ u = x $ , $ dv = e^{2x} dx $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$$\frac{1}{2} x e^{2 x}-\frac{1}{4} e^{2 x}$$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Campbell University

Harvey Mudd College

Idaho State University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

03:51

Evaluate the integral usin…

04:41

evaluate the integral usin…

01:58

02:03

01:59

01:10

01:01

Evaluate the integral by m…

01:34

02:51

Evaluate the integrals usi…

Okay, so for this question we need to evaluate the integral you've, seen integration by parts so and with the indicated choice of u and d v. So basically, u and v are given. We need to solve for u and v and u, we already know equals to x. So, let's find out what the differential of v goes to e to the power 2 x dx, as we can see, there's a difference showing us in front of this v. So all we need to do is bring this inside the differential. In other words, we need to find the anti derivative of this, which is some that d anti duative of e to the power 2 x is just the 1 half e to the power 2 x. So as we can see our vos to the half e to the power 2 x, so this we can rewrite the integral by u d v and by the formula of integration by parts. This is just a: u v! Minus t d! U now we just plug in our? U and v, o? U is its x times 1 half times e to the power 2 x, 2 x minus their ration of 1, half e to the power 2 x d, or u s x is dx. So we know the antidote of this thing is just a line for alpha to the power 2 x, so this will be a half to copy down the first term, minus 1 quarter e to the power 2 x. Okay- and this will be our answer-

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:11

'Find the value of x(a) 409(b) 609(c) 359(d) 1809'…

01:04

'8(a) In the given figure, find value of a, b and c.'

01:23

'simplify the following and write it in exponential formplz help I will…

01:40

'The map below shows the town of Cedarville. In Cedarville, of the area…

00:34

'solve it and please give appropriate answerQuestion 4 Zeba wants t…

'Matt wants to play in the sandpit, and then try the swings, the slide,…

01:25

'Please answer the following question and give a full explanation.E…

05:58

'solve withoit spammingQt Sole (c 7 ` {4+5+5 0 +b+ X2 + X -2 Y…

"plz.. answer the questionsQuestlon Zeba wants t0 place her tour c…

02:55

'the amount of money in an account may increase due to rising stock pri…