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Math Help - Finding A Definete Integral (Without Int. by Parts)

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    Finding A Definete Integral (Without Int. by Parts)

    I need to find the definite integral between 4 and 9 where the function is [1+sqrt(x)]/sqrt(x) dx

    Without using integration by parts. I got 35*1/3 but I'm sure the way I did this was wrong.
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  2. #2
    Eater of Worlds
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    You don't need parts or any other techniques, just plain ol' strightforward integration.

    \frac{1+\sqrt{x}}{\sqrt{x}}=x^{\frac{-1}{2}}+1

    \int_{4}^{9}\left[x^{\frac{-1}{2}}+1\right]dx=7
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by SportfreundeKeaneKent View Post
    I need to find the definite integral between 4 and 9 where the function is [1+sqrt(x)]/sqrt(x) dx

    Without using integration by parts. I got 35*1/3 but I'm sure the way I did this was wrong.
    Or if you meant something like

    \int_a^{b}\frac{(1+\sqrt{x})^n}{\sqrt{x}}dx=2\int_  a^b\frac{(1+\sqrt{x})^n}{2\sqrt{x}}dx=\frac{2(1+\s  qrt{x})^{n+1}}{n+1}\bigg|_{a}^b
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