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Math Help - Double integral

  1. #1
    s7b
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    Double integral

    I don't understand what my limits of integration will be after reversing the order of this double integral;

    integral(from x=0 to x=3) integral(from y=sqrt(x/3) to y=1) of e^(y^3) dydx
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  2. #2
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    R=\left\{ (x,y)\in {{\mathbb{R}}^{2}}|0\le x\le 3,\,\sqrt{\frac{x}{3}}\le y\le 1 \right\}.

    You can describe the same region by just making a sketch. Or try to prove that 0\le x\le 3{{y}^{2}}\le 3 so R=\left\{ (x,y)\in {{\mathbb{R}}^{2}}|0\le x\le 3{{y}^{2}},\,0\le y\le 1 \right\}.
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    Quote Originally Posted by s7b View Post
    I don't understand what my limits of integration will be after reversing the order of this double integral;

    integral(from x=0 to x=3) integral(from y=sqrt(x/3) to y=1) of e^(y^3) dydx
    Have you drawn a clearly labelled diagram that shows the region of the xy-plane that you're integrating over?
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