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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

$\displaystyle \int^{\infty}_0 \sqrt{y} e^{-y^2} dy $

onwards, the substitution $\displaystyle y^3 =x $ is used, and this is what is found after substitution:

$\displaystyle \frac{1}{3} \int^{\infty}_0 x^{-\frac{1}{2}} e^{-x} $

and this is what i get:

$\displaystyle \frac{1}{3} \int^{\infty}_0 x^{-\frac{1}{2}} e^{-x^{\frac{2}{3}}} $

what is wrong?

Re: substitution in gamma integral

Just a typo in that book. The integral should be $\displaystyle \int_0^{\infty}\sqrt{y}e^{-y^3}\;dy$

Re: substitution in gamma integral

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

cheers