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If f and g are continuous functions on [...

If `f and g` are continuous functions on `[0, a]` such that `f(x) = f(a - x) and g(x) + g(a - x)=2,` then show that `int_0^a f(x)g(x) \ dx = int_0^a f(x) \ dx`.

A

`int_(0)^(a)f(x)dx`

B

`int_(0)^(a)g(x)dx`

C

0

D

`int_(0)^(a//2)f(x)dx`

Text Solution

Verified by Experts

The correct Answer is:
A
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