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 286: 8



Work Step by Step

$f(x)=-x^2+x+20$ $and$ $g(x)=x^2-5x$ $When$ $f(x)=g(x),$ $x=-2,5$ $A=\int_{4}^5(f(x)-g(x))dx+\int_5^8(g(x)-f(x))dx$ $A=\int_{4}^5(-2x^2+6x+20)dx+\int_5^8(2x^2-6x+20)dx$ $A=[-\frac{2x^3}{3}+3x^2+20x]_{4}^5+[\frac{2x^3}{3}-3x^2-20x]_5^8$ $A=[-\frac{250}{3}+75+100]-[-\frac{128}{3}+48+80]+[\frac{1024}{3}-192-160]-[\frac{250}{3}-75-100]$ $A=[\frac{275}{3}]-[\frac{256}{3}]+[-\frac{32}{3}]-[-\frac{275}{3}]$ $A=\frac{262}{3}$
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