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Mathematics
Mathematics
Problem
Evaluate numerically (to three decimal places) the integral
1
2
∫
0
π
(
2
+
2
sin
θ
)
2
d
θ
\frac12\int_{0}^{\pi}\bigl(2+2\sin\theta\bigr)^{2}\,d\theta
2
1
∫
0
π
(
2
+
2
sin
θ
)
2
d
θ
that represents the area enclosed by the curve
r
=
2
+
2
sin
θ
r=2+2\sin\theta
r
=
2
+
2
sin
θ
for
0
≤
θ
≤
π
0\le\theta\le\pi
0
≤
θ
≤
π
.
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