$$\int\limits_{-1/2}^{1/2} \cos(2\pi t) e^{-jwt} dt $$ I just got this on test, but unfortunately i could not solve it, i used the integration by parts twice but i did not get the solution. help guys ?

Question

$$\int\limits_{-1/2}^{1/2} \cos(2\pi t) e^{-jwt} dt $$  I just got this on test, but unfortunately i could not solve it, i used the integration by parts twice but i did not  get the solution. help guys ?

mr.math · Answer

Call the given integral $I$, then after integrating twice by parts you will get two equations in two variables one of which is $I$. Solve for it.

anonymous · Answer

well, I did not think about this I think you are right, i will try to solve it again.

mr.math · Answer

Good luck.

anonymous · Answer

thanks bro, i appreciate it.