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Math Help - integration by substitution!

  1. #1
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    integration by substitution!

    evaluate \int\frac{\sin\sqrt{x}{\sqrt{x}dx

    pls somebody should help on the equation above, confuse, thanks
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  2. #2
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    Re: integration by substitution!

    Did you mean \int\frac{\sin\sqrt{x}}{\sqrt{x}}dx ?

    use u=\sqrt{x}.

    Oh and put
    Code:
    [tex]...........[ /tex]
    around your LaTeX.
    Thanks from lawochekel
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  3. #3
    MHF Contributor Siron's Avatar
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    Re: integration by substitution!

    \int \frac{\sin\left(\sqrt{x}\right)}{\sqrt{x}}dx
    Let \sqrt{x}=t
    Thanks from lawochekel
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  4. #4
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    Re: integration by substitution!

    Quote Originally Posted by lawochekel View Post
    evaluate \int\frac{\sin\sqrt{x}{\sqrt{x}dx

    pls somebody should help on the equation above, confuse, thanks
    I=\int \frac{\sin{\sqrt x}}{\sqrt x} \,dx

    \sqrt x =t \Rightarrow \frac{1}{2\sqrt x} dx=dt \Rightarrow \frac{1}{\sqrt x} dx=2dt

    Hence :

    I=2\cdot \int \sin t\,dt=-2\cdot \cos t +C=-2\cdot \cos{\sqrt x} +C
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