Problem

Evaluate the integral. $ \displaystyle \int^2_…

01:48

Problem 21 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int^3_{-2} (x^2 - 3) \,dx $

Answer

$-\frac{10}{3}$

More Answers

00:42

Frank L.

00:46

Amrita B.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Discussion

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Video Transcript

Okay, so this is definitely a girl. We're going to take the anti derivative of this term inside here X squared minus three. And then apply the net change there. So we can start with the anti derivative of X squared X cubed over three. and then for three just That would be three x. Right upper bound of three. Lower negative too. So now we can write this as. So your plan that changed theorem plugging three for X. We get three cubes over three -3 times three. It's the first term. And then subtract negative two cubed over three. Why is three times negative two sort of valuing this? We can get three cubed just 27 over three Most three times 3 is nine from this. We subtract negative two cubed. Um She'll be negative 8/3 -3 times. To give to some minus negative six which would just be plus six. But now 27/3 is nine so 9 -9. This first term will cancel out. So we get negative negative eight over three, then Get a common denominator. We can change this six into 18 over three, so 18/3 minus 8/3 will be 10/3 to add that negative side in front. Get negative 10/3 as our answer.

Joseph R.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Caleb E.

Baylor University

Michael J.

Idaho State University

Joseph L.

Boston College