Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 5 - Applications of Integration - 5.2 Volumes - 5.2 Exercises: 22

Answer

-3

Work Step by Step

Take the antiderivative of $x^{2}$-4x+2 to get $\frac{1}{3}$$x^{3}$-$\frac{4}{2}$$x^{2}$+2x. This simplifies to $\frac{1}{3}$$x^{3}$-2$x^{2}$+2x. Plug in the upper and lower bounds to get [$\frac{1}{3}$$4^3$-2($4^2$)+2(4)] - [$\frac{1}{3}$$1^3$-2($1^2$)+2(1)]. This simplifies to [$\frac{64}{3}$-32+8] - [$\frac{1}{3}$-2+2]. Finally, we simplify to [$\frac{64}{3}$-$\frac{72}{3}$] - [$\frac{1}{3}$], which equals $\frac{-9}{3}$ or -3.
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