Question

Triple integrals. Changing the limits of intergration.

Answer 1

Find at least two different limits of integration for the following triple integral.

\[\int\limits_{0}^{1}\int\limits_{0}^{x^2}\int\limits_{0}^{x} f(x,y,z) dzdydx\]

Answer 2

draw a sketch of the region that your integrating over, then you can read off limits of integration in any order you would like.

Answer 3

How about algebraically? When drawing is too difficult.

Answer 4

@Redcan

Answer 5

My implied inequalities are

Answer 6

It looks like you can solve you ineq. in terms of the other variables. In this case, you can check with a sketch. really complex regions might be a problem, I don't remember ever dealing with them.

Answer 7

idk.

Answer 8

Can you check my picture for accuracy after I draw it?
@Redcan

Answer 9

also, will I draw it plane-by-plane (xy,zy,xz) or in 3D?

Answer 10

plane by plane should work.