Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - Chapter Review - Review Exercises - Page 417: 22

Answer

$$6x - \frac{{{x^3}}}{3} + C$$

Work Step by Step

$$\eqalign{ & \int {\left( {6 - {x^2}} \right)} dx \cr & {\text{use multiple constant rule }}\int {k \cdot f\left( x \right)} dx = k\int {f\left( x \right)} dx \cr & = \int 6 dx - \int {{x^2}dx} \cr & {\text{use power rule }}\int {{x^x}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \cr & = 6\left( {\frac{{{x^{0 + 1}}}}{{0 + 1}}} \right) - \frac{{{x^{2 + 1}}}}{{2 + 1}} + C \cr & {\text{simplifying}} \cr & = 6\left( x \right) - \frac{{{x^3}}}{3} + C \cr & = 6x - \frac{{{x^3}}}{3} + C \cr} $$
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