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Math Help - Integral of a quotient

  1. #1
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    Integral of a quotient

    The question:
    Find the integral of \int^9_4{\frac{x^3 - x}{x^{\frac{3}{2}}}}

    I'm not sure where to start. My first thought was to split it into two integrals like so:

    \int^9_4(x^3 - x) \int^9_4{\frac{1}{x^{\frac{3}{2}}}}

    But from what I can tell, you cannot split an integral like that. Any ideas? Thanks.
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  2. #2
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    Quote Originally Posted by Glitch View Post
    The question:
    Find the integral of \int^9_4{\frac{x^3 - x}{x^{\frac{3}{2}}}}

    I'm not sure where to start. My first thought was to split it into two integrals like so:

    \int^9_4(x^3 - x) \int^9_4{\frac{1}{x^{\frac{3}{2}}}}

    But from what I can tell, you cannot split an integral like that. Any ideas? Thanks.
    Sorry, but what you have done is very wrong. Would you find \displaystyle \int x^2 \, dx by splitting it up as \displaystyle \int x \, dx \int x \, dx ?

    You are expected to note that \displaystyle \frac{x^3 - x}{x^{3/2}} = \frac{x^2 - 1}{x^{1/2}} = \frac{x^2}{x^{1/2}} -   \frac{1}{x^{1/2}} = x^{3/2} - x^{-1/2}.
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  3. #3
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    Ahh yes, I realised I could do that not long after posting. >_<

    Just to be sure, does this look correct?

    ^9_4[\frac{2}{7}x^{\frac{7}{2}}] -  ^9_4[-2x^{\frac{1}{2}}]
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  4. #4
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    Quote Originally Posted by Glitch View Post
    Ahh yes, I realised I could do that not long after posting. >_<

    Just to be sure, does this look correct?

    ^9_4[\frac{2}{7}x^{\frac{7}{2}}] - ^9_4[-2x^{\frac{1}{2}}]
    No. The first term is wrong and the second term contains an error.

    It should be ^9_4[\frac{2}{5}x^{\frac{5}{2}}] - ^9_4[2x^{\frac{1}{2}}]
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  5. #5
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    Wow, I really am going crazy. >_<

    Thanks.
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