How do I calculate value of integral?
It's given interval $I=[0,5] \times [0,6]$ how do I calculate $\int_{I} −5xy^3 \; d(x,y)$ ?
What is confusing me is that I don't know should I calculate $\int_{0}^{5}\int_{0}^{6} −5xy^3 \; dx \; dy$? or ?
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Since it is rectangular, the order in which you integrate doesn't matter. – Kaynex Nov 18 '16 at 17:18
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I get different solutions @Kaynex – Alen Nov 18 '16 at 17:21
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Your bounds have to match your variable. When you integrate y, it should be from 0 to 6. So if you switch the order, you should switch the bounds. – Kaynex Nov 18 '16 at 17:24
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If switching the order gives you a different result, you've done at least one of the computations wrong. You haven't included this work in your question; if you edit it to include such, you're more likely to get a helpful response. – Semiclassical Nov 18 '16 at 17:26
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Your example above has the wrong bounds. – Kaynex Nov 18 '16 at 17:26
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Oh so I should but dydx? @Kaynex – Alen Nov 18 '16 at 17:36
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dydx if you want to keep your bounds as above. dxdy if you switch the bounds. Both should work. – Kaynex Nov 18 '16 at 17:50
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$\int_{[0,5]\times [0,6]} (−5xy^3) d(x,y)= \int_{0}^{5}\int_{0}^{6}( −5xy^3)dxdy$ which is the same as $\int_{0}^{6}\int_{0}^{5}( −5xy^3)dydx$ – user90369 Nov 18 '16 at 17:55