How to Determine and Visualize Integration Limits in 3D Surfaces?

[BrownianMan]

Find the volume lying below z = 3 - 2y and above z = x^2 + y^2.

How would I go about finding the limits of integration for this problem?

 

[LCKurtz]

Set the z's equal and plot the resulting xy equation in the xy plane to figure out the limits.

 

[BrownianMan]

Thanks.

What if the question did not specify that z = 3 - 2y was above z = x^2 + y^2? How would I determine that it was in fact above it? I'm having some trouble visualizing all of this in 3 dimensions.

 

[LCKurtz]

Thanks.

What if the question did not specify that z = 3 - 2y was above z = x^2 + y^2? How would I determine that it was in fact above it? I'm having some trouble visualizing all of this in 3 dimensions.

The usual way to help visualize things like this is to draw a picture of the surface. You should be able to recognize one as a paraboloid and the other a plane.