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Mathematics
Mathematics
Problem
Prove that
∫
0
π
/
2
d
x
(
a
2
sin
2
x
+
b
2
cos
2
x
)
2
=
π
(
a
2
+
b
2
)
4
a
3
b
3
\int_{0}^{\pi/2} \frac{dx}{(a^2 \sin^2 x + b^2 \cos^2 x)^2} = \frac{\pi(a^2 + b^2)}{4a^3 b^3}
∫
0
π
/2
(
a
2
sin
2
x
+
b
2
cos
2
x
)
2
d
x
=
4
a
3
b
3
π
(
a
2
+
b
2
)
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