Integrating f(x) = sinx and Finding A(w) Using Product-to-Sum Formula

[kasse]

Homework Statement

Represent

f(x)
= sinx if 0 < x < pi
= 0 if x > pi

as an integral

The Attempt at a Solution

I first try to find A(w) = $$\int$$(1/pi)sinv cos wv dv between 0 and pi. How on Earth do I solve that integral?

I've tried to use the product-to-sum formula, but the values of the integral depends on the value of w.

 

[Gib Z]

There is an overlap is the definition of your function.

 

[kasse]

Corrected