MHB Solving Double Integrals: Order of Integration Explained

[Estelle]

Hey guys,

need your help and hope someone takes the time:

I need to solve the double integral by changing the order of Integration.

View attachment 4966

I would really appreciate if you could illustrate the way of how to compute the solution.

Best
Estelle :)

 

[MarkFL]

Hello and welcome to MHB, Estelle! :D

I have moved this thread, since it is a problem more likely found in the 3rd semester of an elementary calculus course.

Are you certain the problem isn't actually:

$$\int_{-3}^1\int_{2x}^{3-x^2}xy\,dy\,dx$$?

 

[Prove It]

Assuming that what Mark has posted is correct, to reverse the order of integration you need to SKETCH the region of integration, and then figure out your bounds by using horizontal strips instead of vertical ones...