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Mathematics
Mathematics
Problem
Prove that
∫
0
a
f
(
x
)
d
x
=
∫
0
a
f
(
a
−
x
)
d
x
\int_{0}^{a} f(x) dx = \int_{0}^{a} f(a-x) dx
∫
0
a
f
(
x
)
d
x
=
∫
0
a
f
(
a
−
x
)
d
x
and hence evaluate
∫
0
π
2
cos
5
x
sin
5
x
+
cos
5
x
d
x
\int_{0}^{\frac{\pi}{2}} \frac{\cos^5 x}{\sin^5 x + \cos^5 x} dx
∫
0
2
π
s
i
n
5
x
+
c
o
s
5
x
c
o
s
5
x
d
x
. (M-19)
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