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Compute this integral?

image.jpgDoing a project before going to uni as part of my offer, have 2 days left but stuck on this part..
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plug it into software, request steps, copy, get university place.
Original post by Connahnieurzyla
image.jpgDoing a project before going to uni as part of my offer, have 2 days left but stuck on this part..


I think the upper limit is supposed to be ∞\infty rather than −∞-\infty.

To solve this, first note that if I=∫−∞∞e−x2dxI = \int_{-\infty}^{\infty}e^{-x^2} dx, then I2=∫−∞∞e−(x2+y2)dxdyI^2 = \int_{-\infty}^{\infty} e^{-(x^2+y^2)}dxdy. Now you can use polar co-ordinates to evaluate this. A simple change of co-ordinates will then transform this into the question you've been given.

Can I ask what course and university you're doing/ going to?
(edited 8 years ago)
Original post by brittanna
I think the upper limit is supposed to be ∞\infty rather than −∞-\infty.

To solve this, first note that if I=∫−∞∞e−x2dxI = \int_{-\infty}^{\infty}e^{-x^2} dx, then I2=∫−∞∞e−(x2+y2)dxdyI^2 = \int_{-\infty}^{\infty} e^{-(x^2+y^2)}dxdy. Now you can use polar co-ordinates to evaluate this. A simple change of co-ordinates will then transform this into the question you've been given.

Can I ask what course and university you're doing/ going to?


Thanks very much, I'll look at this properly tomorrow morning when I'm functioning and I'm going to Newcastle for Mathematics bsc :smile:

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