Will This Integral Give a Pretty Answer?

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SUMMARY

The integral ∫exp(-x^2/k) *cos(2*pi*s*x) dx from -infinity to infinity evaluates to a closed-form solution, specifically yielding a "pretty answer" when computed with the specified limits. This integral is related to the error function, but the definite integral from -infinity to infinity simplifies the evaluation significantly. Users are encouraged to perform the calculation to observe the elegant result directly.

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∫exp(-x^2/k) *cos(2*pi*s*x) dx from -infinity to infinity

So this integral is an error function unless I take the definite integral from -infinity to infinity.

Will this give me a pretty answer in I do this with the limits specified?
 
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richard7893 said:
∫exp(-x^2/k) *cos(2*pi*s*x) dx from -infinity to infinity

So this integral is an error function unless I take the definite integral from -infinity to infinity.

Will this give me a pretty answer in I do this with the limits specified?

Yes, it will; try it and see.
 

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