# Double integralWatch

#1
Defining I as the integral of exp(-x^2) dx, with limits minus infinity to infinity, and considering I^2 as a double integral over the whole plane, evaluate I.
Hence find Int (x^n exp(-x))dx with limits 0 to infinity, when n =1/2 and 2/3.

Can anyone pls give me some idea as to how i should be doing this problem?
thanks
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12 years ago
#2
The first problem:
Consider switching to polar coordinates to find I^2
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#3
sorry i dont understand exactly how to express I^2 as a double integral, or how i should convert to polars. and what are the limits? Are they 0 to inf for r, and 0 to 2pi for theta?
thanks for any help
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12 years ago
#4
The limits are correct. Do you know how to find the Jacobian when you're changing coordinates?

I^2 = INT INT exp(-x^2-y^2) dxdy
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