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.

$ \displaystyle \int^{1}_{-1} t(1 - t)^2 \,dt $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$-\frac{4}{3}$

01:18

Frank Lin

00:58

Amrita Bhasin

03:19

Joseph Russell

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Missouri State University

Harvey Mudd College

Baylor University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

0:00

Evaluate the integral.…

09:43

Evaluate the definite inte…

01:52

evaluate the definite inte…

01:02

00:39

09:55

03:06

01:14

Evaluate the given integra…

to evaluate the definite integral from negative 1 to 1 of three times one minus t squared DT. We apply substitution and here we let U equal to one -T. And so D you is just negative DT or that negative do you? Is equal to DT? We want to change the balance from T to you. So if T is equal to negative one then we have U equal to one minus negative one, that's equal to two. And if T is one we have U equal to 1 -1, that's equal to zero. And so we rewrite our integral into the integral from 2-0 of tee times we have one minus T. That's you raised to the second power times DT which is negative. Do you? Now? We still want to change T here and you will do that using the substitution that we had, If U is equal to 1 -5. Then from here we can say that T is equal to one minus you. And so we changed that and we have the integral from 2-0 of one minus you times you squared times negative. Do you now note that if we have the integral from A to B of F of X dx this is the same as the negative of the integral from B to A of F of x dx. We're going to flip this and we have the negative of the integral from 0 to 2 of U squared minus You to the 3rd power times negative do you? Which is the same as the integral from 0 to 2 of you squared minus U. To the third power do you? And here we integrate and we get You raised to the 3rd power over 3-. You do the forest power over four. This evaluated from 0 to 2. Now if us to we have to to the third power over sweet -2 to the 4th power over four. This minus when you is zero Which becomes zero eventually. And so we have 8/3 minus 16/4 or four. And this gives us the value of 8 -12/3. Or that's just Negative for over three. So this is the value of the integral.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:45

Select the correct answer.Which statement describes the end behavior of …

02:32

A farmer milks 16 cows every hour. The size of his herd varies as new calves…

00:33

a car dealership pays a wholesale price of $12,000 to purchase a vehicle. Th…

00:59

If a car travels at an average speed of x miles per hour, how far would the …

01:00

Help ASAP Plz !!!! A windowpane is 6 inches by 6 inches. What is the dis…

01:16

a container of candy is shaped like a cylinder and has a volume of 125.6 cub…

01:49

PLEASE HELPDora calculated the mean absolute deviation for the data set 35, …

The diameter of a cylinder is 4 centimeters. The height is 12 centimeters. U…

03:13

A salesman used three types of order forms: A, B, C. He used 40 of Form A. O…

01:01

To visit her grandmother, Melek takes a motorcycle 3.83.83, point, 8 kilomet…