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: 2


$A=\frac{34}{3} $

Work Step by Step

$f(x) = 3x+8$ $and$ $g(x) =x^2+2x+2$ $A= \int_0^2 [(3x+8)-(x^2+2x+2)]dx $ $A= \int_0^2 [-x^2+x+6]dx $ $A= [-\frac{1}{3}x^3+ \frac{1}{2} x^2 +6x]_0^2 $ $A= [-\frac{8}{3} +2+12]-0 $ $A= [-\frac{8}{3}+\frac{6}{3} + \frac{36}{3}] $ $A= \frac{34}{3} $
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