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Solved: For The Integral, inttegral 4_0 Integral x _0, e
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Next we change to polar form: x2y2r2, dx, dydAr,dtheta, dr, therefore beginalign I2 iint e-(r2)r,dtheta, dr int_02pileft(int_0infty re-r2drright)dtheta 2piint_0infty re-r2dr endalign.
Just bear in mind that this is simpler than obtaining a definite integral of the Gaussian over some interval (a,b and we still cannot obtain an antiderivative for the Gaussian expressible in terms of elementary functions).
K sqrt ncdot frac pi (2n-3)!2(2n-2)!