Chapter 6 - Applications of the Integral - 6.1 Area Between Two Curves - Exercises - Page 286: 3

$A=\frac{32}{3} $

$f(x) = x^2 +2$ $and$ $g(x) = 2x+5$ $When$ $f(x) =g(x),$ $x =-1,3$ $A=\int_{-1}^3 (g(x)-f(x))dx $ $A=\int_{-1}^3 (-x^2 +2x +3)dx $ $A= [-\frac{1}{3} x^3 +x^2 +3x]_{-1}^3 $ $A=[-\frac{27}{3}+9+9]-[\frac{1}{3} +1-3] $ $A=[9]-[-\frac{5}{3}] $ $A=\frac{32}{3} $