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Mathematics
Mathematics
Problem
Prove that
∫
0
π
x
f
(
sin
x
)
d
x
=
π
2
∫
0
π
f
(
sin
x
)
d
x
\int_{0}^{\pi} x f(\sin x) dx = \frac{\pi}{2} \int_{0}^{\pi} f(\sin x) dx
∫
0
π
x
f
(
sin
x
)
d
x
=
2
π
∫
0
π
f
(
sin
x
)
d
x
.
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