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^3_{-2} (x^2 - 3) \,dx $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Joseph Russell
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
00:42
Frank Lin
00:46
Amrita Bhasin
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
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.
08:05
01:16
Evaluate the integral.…
03:58
0:00
Evaluate the definite inte…
02:53
01:43
02:40
06:06
04:14
Evaluate the given integra…
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.
View More Answers From This Book
Find Another Textbook
04:31
company manufactures and sells cellphones per week: The weekly price-demand …
04:44
fish-processing company is concerned about the shelf life of its new cat foo…
02:08
Consider the following statements.If we are testing for the difference b…
02:22
point) Find the velocity u(t) and the speed Ilo(t)|l of particle with positi…
02:29
restaurant: waitress_ Rebecca $ daily wage is Rebecca and Matt work at small…
01:53
Suppose tnat the sitting back-to-knee length for a group of adults has norma…
03:40
In the country of United States of Heightlandia, the height measurements of …
01:59
#3.A test is normally distributed with the mean of 40 and the standard devia…
04:53
1. Jim has 3 pairs of pants, 2 shirts, and 2 hats. Use the Fundamental Count…
01:50
What two positive real numbers whose product is 68 have the smallest possibl…