Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 409: 21



Work Step by Step

Original Equation: $\int$ $(x^{2}-3)dx$ on the interval $[3,-2]$ To solve this integral, we first need to find the anti-derivative. The anti-derivative of $x^{n}$ is found through the equation $\frac{x^{n+1}}{n+1}$. by applying this formula to each term in the equation, we see that the final anti-derivative is $\frac{x^{3}}{3}-3x$ Now that we have this equation, we simply subtract the bottom range from the upper range. Our range is $[3,-2]$, so we plug 3 and -2 into the anti derivative and the difference of the two is our final answer. $(\frac{3^{3}}{3}-3(3))$-$(\frac{-2^{3}}{3}-3(-2))$ $= \frac{-10}{3}$
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