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Math Help - Integration problem with impossible integral

  1. #1
    Senior Member x3bnm's Avatar
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    Integration problem with impossible integral

    I found an integration problem for which I can't find the answer from the top my head. Is there an easy way to integrate the following integral?
    <br />
\int_0^a \frac{x^3}{\sqrt{a^2-x^2}} dx<br />

    Thanks.
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  2. #2
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    Krizalid's Avatar
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    note that x^3=x^2\cdot x, so put t^2=a^2-x^2.
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    note that x^3=x^2\cdot x, so put t^2=a^2-x^2.
    Why bother .... The OP said the integral was impossible ....! I don't know why anyone would want to try and do an impossible integral. (Now, if it was an integral that was difficult for the OP, then that would be a different matter ....)
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  4. #4
    Super Member 11rdc11's Avatar
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    Try the trig sub x =a\sin{\theta}

    it simplifies to

    a^3\int \sin^3{\theta}d\theta
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  5. #5
    Senior Member x3bnm's Avatar
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    Thank you all for your input. Yes at last i solved this integral. I tried both 11rdc11 and Krizalid's way. Both procedures work.
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  6. #6
    Math Engineering Student
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    Quote Originally Posted by mr fantastic View Post
    Why bother .... The OP said the integral was impossible ....! I don't know why anyone would want to try and do an impossible integral. (Now, if it was an integral that was difficult for the OP, then that would be a different matter ....)
    ahaha, no matter, actually i just read "integration" and then decided to post.
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