Download the App!

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

Question

Answered step-by-step

Evaluate the integral.

$ \displaystyle \int te^{-3t} dt $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Danjoseph Quijada

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Missouri State University

Harvey Mudd College

Baylor University

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.

01:18

Evaluate the integral. Eva…

01:30

03:07

Evaluate definite integral…

01:23

'Evaluate the followi…

02:02

00:50

Evaluate the integral te3t…

0:00

01:46

Evaluate the definite inte…

01:02

04:33

03:11

01:33

03:28

Evaluate $\int_{0}^{3}\lef…

09:43

02:23

Evaluate the integral.…

03:06

00:41

Evaluate the indefinite in…

Hello. So we're trying to evaluate into girl of t E to a native three tt This is a standard integration by parts problem. So you have to figure out a you and a devi to decompose the problem with. Usually you want to find a you that you khun keep differentiating until you get to like one. So that you, Khun, basically get rid of it. And the DV needs to be something that you can integrate visioning your conventional methods. So in this case, it's easy to see the U equals T and D vehicles even Eva three t I say easy because I've done this so many times. It comes with experience. Do you would then be equal to DT? The is equal to e to the negative one third e to the negative three t So what happens next? Put it together. I color coded it. So it's easier to see I put the constants in France. It's easier to work with afterwards, So you have equals to you tempt me which is they won thirty to the in the eternity of three t minus then ago VD you So that's minus ah native one third in a girl of eighteen eighty three T d. T. So you get a plus one third in the next line. Um, and then integrating into ninety three t by itself would just would he also give you another native one third term in a man we get eked native one thirty, eatin a three T minus one ninth eater native three t plus C.

View More Answers From This Book

Find Another Textbook