Change the order of integration to solve tricky integrals

The double integral over a region can be expressed in two different ways. It could be that we write dxdy which means that we integrate with respect to x first and then y (called horizontal strip). Or it could be dydx which means y is integrated first and then x (vertical strips). The big idea is we can convert between these and so can choose whichever is the easier of the two. The steps are:
1) Given an integral, sketch the region implied by the limits of integration
2) Now interpret that region the opposite way, such as vertical strips instead of horizontal strips
3) Write the new integral in the opposite order of integration
4) Hopefully it will now be easier to compute!

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