BrownianMan
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Reversing Order of Integration: Double Integral Evaluation
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![gif.latex?\int_{0}^{8}\int_{\sqrt[3]{y}}^{{2}}7e^{x^4}dxdy.gif](/data/attachments/121/121114-9c5994283ab8624f2d7259db665996dc.jpg?hash=nFmUKDq4Yk){kind=small}
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The first step in this type of problem is to sketch a graph of the region over which integration is taking place. For the inner integral, x ranges from cuberoot(y) to 2. For the outer integral, y ranges from 0 to 8. Sketch the graphs of x = y1/3 and x = 2, and then sketch the graphs of y = 0 and y = 8. For the iterated integral with the opposite order, the inner integration limits will involve two functions of y, and the outer integration limits will involve two x values.BrownianMan said:Evaluate the integral by reversing the order of integration.
![gif.latex?\int_{0}^{8}\int_{\sqrt[3]{y}}^{{2}}7e^{x^4}dxdy.gif](https://www.physicsforums.com/attachments/gif-latex-int_-0-8-int_-sqrt-3-y-2-7e-x-4-dxdy-gif.138033/ "gif.latex?\int_{0}^{8}\int_{\sqrt[3]{y}}^{{2}}7e^{x^4}dxdy.gif")
I'm not exactly sure how to approach this problem. Any help would be appreciated!
BrownianMan
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Ok, so would the answer be
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Yep.