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Double Integrals : Reversing Order of Integration and Sums of Iterated Integrals

Problem 1 and 2: Sketch the region of integration, reverse the order of integration, and evaluate both iterated integrals.
∫0-->2 ∫0-->4-y2 x dx dy
∫0-->pi/2 ∫0-->cosx sin x dy dx

Problem 3: When you reverse the order of integration, you should obtain a sum of iterated integrals. Make the reversals and evaluate.
∫-2-->1 ∫-x-->x2-2 x-y dy dx

Problem 4: Rewrite the given sum of iterated integrals as a single iterated integral by reversing the order of integration, and evaluate.
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Problem 5: evaluate the given iterated integral.
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Please see the attached file for the fully formatted problems.

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Solution Summary

Double Integrals, Reversing Order of Integration and Sums of Iterated Integrals are investigated. The solution is detailed and well presented.

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