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Math Help - Double integral area

  1. #1
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    Double integral area

    Evaluate Double Integral sin(y^3)dA where R is the region bounded by y=x^1/2, y=2, x= 0


    I've set up the integral from x^1/2 to 2 and the other integral from 0 to 4.
    I've also reversed the order and got 0 to y^2 and 0^2 and both times I end up having to integrate sin(y^3) which is a massive problem. What am I doing wrong with this problem?
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  2. #2
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    Quote Originally Posted by Calc19Matt View Post
    Evaluate Double Integral sin(y^3)dA where R is the region bounded by y=x^1/2, y=2, x= 0


    I've set up the integral from x^1/2 to 2 and the other integral from 0 to 4.
    I've also reversed the order and got 0 to y^2 and 0^2 and both times I end up having to integrate sin(y^3) which is a massive problem. What am I doing wrong with this problem?
    You can integrate \int_0^1 \int_0^{y^2} \sin y^3 \, dx\,dy with respect to x readily.
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    Am I doing it wrong because then I get Integral sin(y^3)y^2. how do i integrate that?
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    U-substitution: if u=y^3, then du=3y^2\,dy.

    --Kevin C.
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