Reversing Order of Integration: Double Integral Evaluation

BrownianMan · Nov 25, 2010

Evaluate the integral by reversing the order of integration.

$gif.latex?\int_{0}^{8}\int_{\sqrt[3]{y}}^{{2}}7e^{x^4}dxdy.gif$

I'm not exactly sure how to approach this problem. Any help would be appreciated!

Mark44 · Nov 25, 2010

BrownianMan said:

Evaluate the integral by reversing the order of integration.

$gif.latex?\int_{0}^{8}\int_{\sqrt[3]{y}}^{{2}}7e^{x^4}dxdy.gif$

I'm not exactly sure how to approach this problem. Any help would be appreciated!

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 = y^1/3 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 · Nov 25, 2010

Ok, so would the answer be

$gif.latex?\frac{7}{4}\left%20(%20e^{16}-1%20\right%20).gif$

Mark44 · Nov 26, 2010

Reversing Order of Integration: Double Integral Evaluation

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