Q- let T is not zero be a fixed number suppose f is a continuous function such that for all x belongs to R, f(x+T) + f(x). if

I = integration from (T to 0) f(x) dx, then the value of

Integration from (3 to 3+3T) f (2x) dx is?

Dear Kanika,

 given, I = ₀^T∫ f(x) dx

_^3+3T3∫ f(2x) dx  = 3 ₀^T∫ f(2x) dx     where T is the period of func. f(x)

let 2x = t or  2dx = dt

so,  3 ₀^T∫ f(2x) dx =  3[ ₀^T∫ f(t) dt ] /2 = 3I/2

hence,  _^3+3T3∫ f(2x) dx = 3I/2

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All the best.

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