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Math Help - Integrating a fraction

  1. #1
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    Integrating a fraction

    Hi there,

    can somebody help me to integrate the following:

    \int\frac{1}{2y^{\frac{5}{4}}}dy

    I've used Mathcad to find that the answer is

    \frac{-2}{y^{\frac{1}{4}}}

    But I don't know any formulas or equations to use to get to the answer.

    I would really appreciate any help.

    Thanks.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Integrating a fraction

    Quote Originally Posted by Srengam View Post
    Hi there,

    can somebody help me to integrate the following:

    \int\frac{1}{2y^{\frac{5}{4}}}dy

    I've used Mathcad to find that the answer is

    \frac{-2}{y^{\frac{1}{4}}}

    But I don't know any formulas or equations to use to get to the answer.

    I would really appreciate any help.

    Thanks.

    \int\frac{1}{2y^{\frac{5}{4}}}dy=\frac{1}{2}\int y^{-\frac{5}{4}}dy
    Last edited by Also sprach Zarathustra; June 30th 2011 at 05:06 PM.
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  3. #3
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    Re: Integrating a fraction

    Quote Originally Posted by Srengam View Post
    Hi there,

    can somebody help me to integrate the following:

    \int\frac{1}{2y^{\frac{5}{4}}}dy



    I've used Mathcad to find that the answer is

    \frac{-2}{y^{\frac{1}{4}}}

    But I don't know any formulas or equations to use to get to the answer.

    I would really appreciate any help.

    Thanks.
    First write the integral using a negative index before applying the
    power rule of integration.

    \frac{1}{2}\int{\frac{1}{y^{\frac{5}{4}}}dy=\frac{  1}{2}\int{y^{-\frac{5}{4}}}dy

    Now increase the index of y by 1 and divide by the new index.
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  4. #4
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    Re: Integrating a fraction

    Quote Originally Posted by Archie Meade View Post

    Now increase the index of y by 1 and divide by the new index.
    And add 'c'

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  5. #5
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    Re: Integrating a fraction

    Sorry, now I can't understand how to do the integration

    \int y^{-\frac{5}{4}}dy=\frac{-4}{y^{\frac{1}{4}}}

    I don't what equation or formula to use? I've never had the integrate a fractional power before, and can't find how anywhere in my notes.

    Thanks.
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  6. #6
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    Re: Integrating a fraction

    Quote Originally Posted by Srengam View Post
    Sorry, now I can't understand how to do the integration

    \int y^{-\frac{5}{4}}dy=\frac{-4}{y^{\frac{1}{4}}}

    I don't what equation or formula to use? I've never had the integrate a fractional power before, and can't find how anywhere in my notes.

    Thanks.
    same as the rule for any other exponent (except -1) ...

    \frac{y^{-\frac{5}{4} + 1}}{-\frac{5}{4} + 1} + C
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  7. #7
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    Re: Integrating a fraction

    Thanks all,

    I've been able to work through it now with your help.
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