Answer
$$A = 18\pi $$
Work Step by Step
$$\eqalign{
& \int_{ - 6}^6 {\sqrt {36 - {x^2}} dx} \cr
& {\text{Let }}f\left( x \right) = \sqrt {36 - {x^2}} ,\left( {{\text{graph shown below}}} \right) \cr
& {\text{From the graph we can notice that the area is a semicircle, so}} \cr
& A = \frac{1}{2}\pi {r^2} \cr
& {\text{Where }}r = 6 \cr
& A = \frac{1}{2}\pi {\left( 6 \right)^2} \cr
& A = \frac{1}{2}\pi \left( {36} \right) \cr
& A = 18\pi \cr} $$
