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Math Help - Evaluate integral

  1. #1
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    Evaluate integral

    l don't understand the d/dx in front of the integral...

    \frac{d}{dx}\int^x_0 \frac{du}{1+u^{2}}



    = arctan 0 - arctan x

    = -arctanx

    could this be right?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by algebra2 View Post
    l don't understand the d/dx in front of the integral...

    \frac{d}{dx}\int^x_0 \frac{du}{1+u^{2}}


    = arctan 0 - arctan x

    = -arctanx

    could this be right?
    You need to use the fundemental theorem of calculus

    \frac{d}{dx} \int_{0}^{x}\frac{1}{1+u^2}du=\frac{1}{1+x^2}
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  3. #3
    MHF Contributor matheagle's Avatar
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    there was no reason to integrate and then differentiate, but you made mistakes in your integration....

    Quote Originally Posted by algebra2 View Post
    l don't understand the d/dx in front of the integral...

    \frac{d}{dx}\int^x_0 \frac{du}{1+u^{2}}


    =  {d\over dx} (\arctan x - \arctan 0)

    =  {d\over dx} (\arctan x)

    =  {1\over 1+x^2}

    is right....
    .....NOW, but is unnecessary.
    Last edited by matheagle; May 21st 2009 at 08:15 AM.
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