💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Evaluate the integral.

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

$-\frac{4}{3}$

01:18

Frank L.

00:58

Amrita B.

03:19

Joseph R.

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Oregon State University

University of Nottingham

Idaho State University

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:20

Evaluate the integral.…

09:43

03:05

03:06

01:11

Evaluate the indefinite in…

00:40

03:01

00:47

Evaluate the integrals.

04:13

01:34

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.

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Evaluate the integral.$\int_{-1}^{1} t(1-t)^{2} d t$

$ \displaystyle \int \frac{dt}{(t^2 - 1)^2} $…

$ \displaystyle \int t \csc^2 t dt $

$ \displaystyle \int \frac{\sin^2 \left(\frac…

Evaluate the indefinite integral.$\int\left(t^{1 / 2}+1\right)(t+1) d t$…

Evaluate the integral.$\int_{0}^{1} \frac{4}{t^{2}+1} d t$

Evaluate the integral.$\int \frac{t}{t^{4}+2} d t$

Evaluate the integrals.\begin{equation}\int_{1}^{e^{x}} \frac{1}{t} d t\…

$ \displaystyle \int (sec^2 t i + (t^2 + 1)^3…

Evaluate the integrals.$$\int \frac{1}{t^{2}} \cos \left(\frac{1}{t}-1\r…