substitution in gamma integral

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November 14th 2011, 12:15 AM
phycdude

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substitution in gamma integral

Hi, im trying out a problem in schaum's advanced calculus ans on pg 380, chap. 15, i met this problem:
Evaluate
$\int^{\infty}_0 \sqrt{y} e^{-y^2} dy$
onwards, the substitution $y^3 =x$ is used, and this is what is found after substitution:
$\frac{1}{3} \int^{\infty}_0 x^{-\frac{1}{2}} e^{-x}$

and this is what i get:
$\frac{1}{3} \int^{\infty}_0 x^{-\frac{1}{2}} e^{-x^{\frac{2}{3}}}$

what is wrong?
November 14th 2011, 12:54 AM
FernandoRevilla

Re: substitution in gamma integral

Just a typo in that book. The integral should be $\int_0^{\infty}\sqrt{y}e^{-y^3}\;dy$
November 14th 2011, 01:25 AM
phycdude

Re: substitution in gamma integral

oh, i thought i was making really silly algebra mistakes.
cheers

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