Question

set up the six triple iterated integrals for the volume for the volume of the solid that is bounded by x = 36-9y^2 , y = 2x , x =0, z =0 ( is this just switching the order of integration like dxdydz, dxdzdy...

Answer 1

The hard part is setting up the limits for each case.

Answer 2

However the limits of integration will be different for each order of integration.

Answer 3

You must draw a picture.

Answer 4

I did for one case X: (0,1), y:(x/2,1-x/2) ,Z: (0,2-x-2y)

Answer 5

thanks guys !

Answer 6

I just thought I'd mention, since you sort of hit upon it, is that there are six because 3!=6 because there are 3! ways to arrange three of anything, in this case it's dx, dy, and dz.