Evaluate numerically (to three decimal places) the integral 12 _ 0 ^ (2+2 )^ 2 ,d…

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Evaluate numerically (to three decimal places) the integral

\frac12\int_{0}^{\pi}\bigl(2+2\sin\theta\bigr)^{2}\,d\theta

that represents the area enclosed by the curve

r=2+2\sin\theta

for

0\le\theta\le\pi