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.
Problem 5: evaluate the given iterated integral.
Please see the attached file for the fully formatted problems.
Double Integrals, Reversing Order of Integration and Sums of Iterated Integrals are investigated. The solution is detailed and well presented.