Calculus 8th Edition

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

Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 337: 23

Answer

$-2$

Work Step by Step

We first multiply the two quantities in the integrand, which result in the polynomial $8x^3 - 12x^2 + 2x - 3$ We now can take the integral of this polynomial, which is $2x^4 - 4x^3 + x^2 - 3x$ Now, we substitute the bounds of integration $2$ and $0$ and get the difference $(2(2)^4 - 4(2)^3 + 2^2 - 3(2)) - (0) = 32 - 32 + 4 - 6 = -2$
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