Chapter 4 - Integration - 4.9 Evaluating Definite Integrals By Substitution - Exercises Set 4.9 - Page 340: 19

$$6$$

$$\eqalign{ & {\text{The area is given by}} \cr & A = \int_{ - 1}^1 {\frac{9}{{{{\left( {x + 2} \right)}^2}}}} dx \cr & {\text{Integrate and evaluate}} \cr & A = \left[ { - \frac{9}{{x + 2}}} \right]_{ - 1}^1 \cr & s = - \left[ {\frac{9}{{1 + 2}} - \frac{9}{{ - 1 + 2}}} \right] \cr & {\text{Simplify}} \cr & s = - \left[ {3 - 9} \right] \cr & s = 6 \cr} $$