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Math Help - double integrals problem

  1. #1
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    double integrals problem

    Im doing this problem below:



    here is the solution and i understand everything except how they integrated the r(sqrt(1+r^2)). could anyone point out how they accomplished that? Thank you.

    solution:
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  2. #2
    MHF Contributor harish21's Avatar
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     \displaystyle{\int 2r - r \sqrt{1+r^2} dr = \int 2r dr - \int r \sqrt{1+r^2} dr}

     \displaystyle{\int 2r dr} = 2  \times \dfrac{r^2}{2} = r^2

    for \displaystyle{ \int r \sqrt{1+r^2} dr} use substitution rule by supposing  u = 1+r^2

    So,  du = 2r \mbox{dr} \implies dr = \dfrac{du}{2}
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  3. #3
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    ah, i should of know that.
    Thanks a bunch.
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