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## Homework Statement

I have to prove:

∫(-infinity:infinity) cos(pi*v/2L)*e^-((L-L_av)^2/sqrt(2pi)*sigma^2) dL proportional to

cos(pi*v/2L_av)*e^-(t/tau)^2

tau is some constant, and sigma << L_av.

## The Attempt at a Solution

i can change the integral to 0:infinity, since sigma << L_av. Then i have to look up some integral solution, probably:

∫(0:infinity) cos(bx)*e^-ax^2 dx

I assume i have to do some trick like 1/L approximately L/L_av^2 - but how can i justify that?