# Evaluate integral of Sine function

1. Oct 9, 2006

### muaythai2006

Hello guyz, I am new at this page. I need your help. I can't able to evaluate this integral. intergral of( sin(pi*t/(2T)) e^ -j2*pi*f*t)dt . The lower limit is 0 and the upper limit is 2T ...This is acctually the Fourier transform of sin(pi*t/(2T)) where 0<t<2T ....I could do the fourier transform of this but only if the limit of t is -infinity to infinity...Thanks for your help...

Last edited: Oct 9, 2006
2. Oct 9, 2006

### vsage

Are you familiar with Euler's identity? Consider rewriting $$sin(\frac{ \pi t}{2T} )$$ as $$\frac{1}{2j} (e^{\frac{j \pi t}{2T}} - e^{-\frac{j \pi t}{2T}})$$

(Edit: Fixing the equation, LaTeX)

Last edited by a moderator: Oct 9, 2006