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Let f(x) be a differentiable function sy...

Let `f(x)` be a differentiable function symmetric about `x=2`, then the value of `int_(0)^(4)cos(pix)f'(x)dx` is equal to________.

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The correct Answer is:
0
`f(x)` is symmetrical about line `x=2`
`:.f(2-x)=f(2+x)`
Replacing `x` by `2-x` we get
`f(x)=f(4-x)`
`:. f'=-f'(4-x)`
`:.I=int_(0)^(4)cos(pix)f'(x)dx`
`=int_(0)^(4)cos(4pi-pix)f'(4-x)dx`
`=-I`
`implies2I=0`
`impliesI=0`
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