Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 6 - Applications of the Integral - 6.1 Area Between Two Curves - Exercises - Page 287: 38

Answer

$27$

Work Step by Step

The area under $y=f(x)$ over an interval $[m,n]$ about the x-axis is given by: $Area, A= \int_{-3}^{3} [|x|-x^2+6) \ dx \\ = 2 \int_0^{3} [x-x^2+6] \ dx \\= 2 [\dfrac{ x^{2}}{2}-\dfrac{x^3}{3}+6x]_0^{3} \\= 2 [\dfrac{ (3^{2})}{2}-\dfrac{(3^3)}{3}+(6)(3) ] \\= 27$
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