Integration when given the exact value of an un-integratable function

[nick.martinez]

given that ∫ e^(-x^2) dx=√∏, calculate the exact value of ∫ e^-((x-a)^2)/c dx

limits of integration for both are from negative infinity to infinity.

I don't even know where to start on this one. I know how to integrate regular functions. How can I find the exact value for an integral I can't even integrate?

Please Help

 

[Curious3141]

given that ∫ e^(-x^2) dx=√∏, calculate the exact value of ∫ e^-((x-a)^2)/c dx

limits of integration for both are from negative infinity to infinity.

I don't even know where to start on this one. I know how to integrate regular functions. How can I find the exact value for an integral I can't even integrate?

Please Help

The trick in these problems is to turn the new integral into the known one by a substitution.

Can you think of a sub to turn that integral into $\displaystyle \int_{-\infty}^{\infty} e^{-y^2}dy$?

I'm using y to avoid confusion here. Keep in mind that in a definite integral, the actual variable of integration doesn't matter (it's a dummy).