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If f(x) and g(x) be continuous in the in...

If f(x) and g(x) be continuous in the interval [0, a] and satisfy the conditions `f(x)=f(a-x)` and `g(x)+g(a-x)=a`, then show that `int_(0)^(a)f(x)g(x)dx=(a)/(2)int_(0)^(a)f(x)dx`. Hence find the value of `int_(0)^(pi)xsinxdx`.

Text Solution

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The correct Answer is:
`I=(a)/(2)int_(0)^(a)f(x)dx`
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