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If f(2a-x)=-f(x), prove that int0^(2a)f(...

If `f(2a-x)=-f(x),` prove that `int_0^(2a)f(x)dx=0`

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Given: `f(2a-x)=-f(x)....(i)`
We have to proof `int_0^(2a)f(x)dx=0`
`int_0^(2a)f(x)dx=int_0^a[f(x)+f(2a-x)]dx`
From(i)
`int_0^(2a)f(x)dx=int_0^a[f(x)+(-f(x))]dx`
`int_0^(2a)f(x)dx=int_0^a[f(x)-f(x)]dx`
`int_0^(2a)f(x)dx=int_0^a 0 dx`
`int_0^(2a)f(x)dx=0`
...
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