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Mathematics
Mathematics
Problem
If
f
f
f
and
g
g
g
are continuous functions satisfying
f
(
x
)
=
f
(
a
−
x
)
f(x) = f(a-x)
f
(
x
)
=
f
(
a
−
x
)
and
g
(
x
)
+
g
(
a
−
x
)
=
2
g(x) + g(a-x) = 2
g
(
x
)
+
g
(
a
−
x
)
=
2
, then show that
∫
0
a
f
(
x
)
g
(
x
)
d
x
=
∫
0
a
f
(
x
)
d
x
\int_{0}^{a} f(x) g(x) dx = \int_{0}^{a} f(x) dx
∫
0
a
f
(
x
)
g
(
x
)
d
x
=
∫
0
a
f
(
x
)
d
x
.
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