how to evaluate intergal?

Question

∫ cos 2πt δ(t-2) dt evaluate from 5 to 10

I have no idea how to do this. Please explain

Answer 1

I think you should try integration by parts. Remembert delta(t-2) only has a value at t=2 at other times it has a value of zero. The integral of a delta function is the unit function. Give it a try. If you are still having problems add some comments I will check back later.

Answer 2

int delta(t-2)dt = 1 if the integrating interval contains t=2 . also for any nonsingular real function f(t) Int (f(t) delta(t-2)) = f(2) for any integrating interval which includes t=2 .

In your integral the integrand is always zero since integrating interval is 5-10 doesnot contain point 2 . Therefore the intgral =0