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Math Help - substitution in gamma integral

  1. #1
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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?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: substitution in gamma integral

    Just a typo in that book. The integral should be \int_0^{\infty}\sqrt{y}e^{-y^3}\;dy
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  3. #3
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    Re: substitution in gamma integral

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