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Math Help - multiple integrals reversing order of integration

  1. #1
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    multiple integrals reversing order of integration

    can you solve for me please

    0 to 4(for the 1st integral) y^.5 to 2 (for the 2nd) (x^3 + 1)^0.5 dxdy?
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  2. #2
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    \int_0^4 {\int_{\sqrt y }^2 {\sqrt {x^3  + 1} \,dx} \,dy} .

    Two ways to reverse integration order:

    1. Make a sketch to see where the integral is taken.
    2. Playin' with inequalities.
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  3. #3
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    hello thanks for your reply. I think for the reverse it would be 0 to 2, x^2 to 4 fcn dydx but i do not know how to integrate that fcn. i think that that fcn cannot be integrated with respect to x and that's why you reverse the order. however, i may have done something incorrectly and can't see it, but i'm getting to have to integrate it anyways, but it's counterpart i could deal with via substitution.
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  4. #4
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    It's actually \int_0^2 {\int_0^{x^2 } {\sqrt {x^3  + 1} \,dy} \,dx} .

    So \int_0^2 {x^2 \sqrt {x^3  + 1} \,dx} , and this is very easy, just set z^2=x^3+1.
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  5. #5
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    thanks so much!
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