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Math Help - Integration by trig substitution

  1. #1
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    Integration by trig substitution

    Trying to do the indefinate integral of x^3 * (9-x^2)^1/2 by using the substitution of x = 3 sin u I get 81* integral[ (sin^3 u)(cos u)] but again I appear to be wrong.
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  2. #2
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    x = 3\sin u
    dx = 3\cos u \: du

    \int {\color{red}x^{3}} {\color{blue}\sqrt{9 -x^{2}}} {\color{magenta}dx}
    = \int {\color{red}\left(3\sin u\right)^{3}} {\color{blue}\sqrt{9 - 9\cos^{2} u}} \cdot {\color{magenta}3 \cos u \: du}
    =  \int 27 \sin^{3} u \cdot 3 \sqrt{1 - \cos^{2} u} \cdot 3\cos u \: du
    = 243 \int \sin^{4} u \cdot \cos u \: du

    I think you forgot to make the sub for dx. This last integral should be straightforward. Make the substitution s = sin u and you should be on your way
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  3. #3
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    Thanks for that you are right I had forgot to sub in the dx value. How do you guys use the correct mathmatic symbols in the post?
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  4. #4
    MHF Contributor ebaines's Avatar
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    Quote Originally Posted by Craka View Post
    How do you guys use the correct mathmatic symbols in the post?
    See the sticky in the LaTex help forum.
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