Chapter 6 - Applications of the Integral - 6.1 Area Between Two Curves - Exercises - Page 286: 2

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

$f(x) = 3x+8$ $and$ $g(x) =x^2+2x+2$ $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} $