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Let f(x) be a continuous and periodic fu...

Let `f(x)` be a continuous and periodic function such that `f(x)=f(x+T)` for all `xepsilonR,Tgt0`.If `int_(-2T)^(a+5T)f(x)dx=19(ag0)` and `int_(0)^(T)f(x)dx=2`, then find the value of `int_(0)^(a)f(x)dx`.

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Given that
`int_(-2T)^(a+5T)f(x)dx=19`
`=int_(-2T)^(5T)f(x)dx+int_(5T)^(5T)f(x)dx=19`
`implies7 int_(0)^(T)f(x)dx+int_(0)^(a)f(x)dx=19`
`implies int_(0)^(a)f(x)dx=19-7xx19-14=5`
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