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Math Help - Help with some intergration

  1. #1
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    Help with some intergration

    Hello

    I need help with these 3 intergrations questions please

    thanks

    Kind Regards
    Attached Thumbnails Attached Thumbnails Help with some intergration-untitled.gif  
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by rpatel View Post
    Hello

    I need help with these 3 intergrations questions please

    thanks

    Kind Regards
    1. \begin{aligned}\frac{2x-1}{\sqrt{x-x^2}}&=\frac{2x-1}{\sqrt{\frac{1}{4}(1-(1-4x+4x^2))}}\\<br />
&=\frac{2x-1}{\sqrt{\tfrac{1}{4}(1-(1-2x)^2}}\\<br />
&=\frac{2x-1}{\tfrac{1}{2}\sqrt{1-(1-2x)^2}}\\<br />
&=2\frac{2x-1}{\sqrt{1-(2x-1)^2}}\end{aligned}

    Now just let \varphi=2x-1 and see the next problem.

    2. \int\frac{dx}{\sqrt{1-x^2}}

    Let \sin(\theta)=x

    3. \int\arcsin(x)dx

    Let \arcsin(x)=\varphi
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    1. \begin{aligned}\frac{2x-1}{\sqrt{x-x^2}}&=\frac{2x-1}{\sqrt{\frac{1}{4}(1-(1-4x+4x^2))}}\\<br />
&=\frac{2x-1}{\sqrt{\tfrac{1}{4}(1-(1-2x)^2}}\\<br />
&=\frac{2x-1}{\tfrac{1}{2}\sqrt{1-(1-2x)^2}}\\<br />
&=2\frac{2x-1}{\sqrt{1-(2x-1)^2}}\end{aligned}

    Now just let \varphi=2x-1 and see the next problem.
    ....or you could have made the simple substitution z=x-x^2 which would convert the integral into -\int z^{-\frac{1}{2}}\,dz.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    ....or you could have made the simple substitution z=x-x^2 which would convert the integral into -\int z^{-\frac{1}{2}}\,dz.
    ....nu uh....
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