(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

R(x) := ∫ exp ( -y^2 - x^2/y^2 ) dy

3. The attempt at a solution

I move the derivative operator inside the integral and differentiate with respect to x

R'(x) = ∫ [ - 2x/y^2 ] exp ( -x^2/y^2 - y^2 ) dy

Then I let: t = x/y and dy = - x/t^2 dt

R'(x) = 2 ∫ [ - x ] [ t^2 / x^2 ] exp ( t^2 - x^2/t^2 ) [ - x/t^2 ] dt

=> R'(x) = 2 R(x)

But that last part is supposed to be R'(x) = - 2 R(x) - I don't see why.

Then, it follows that this integrates to R(x) = Ae^(−2x) and x = 0 gives R(0) = √π. This last part I don't get it neither. From where the e^(-2x) came from?

Any help is very appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Differentiation under the integral sign

**Physics Forums | Science Articles, Homework Help, Discussion**