Find the volume of the region.
The region between the cylinder z=y^2 and the xy-plane that is bounded by the planes x=0,x=1,y=-1,y=1
When I graph this it looks like a halfpipe(skateboarding) extending in the positive x direction.
Could someone please help me determine the limits of integration.
int 0..1 int x^2+1.. x^2-1 int 0.. y^2 dz dy dx
That's just a double integral. You're integrating from the x-y plane up to the surface that is . That's the z-direction. And we're integrating that over the foot-print in the x-y plane that's just the two unit squares underneath the surface which because it's symmetric, just multiply by two, the volume underneath the unit square as x goes from 0 to 1 and y goes from 0 to one or:
or if you wanna' be a purist, a triple integral:
but same dif.
I will take the purist direction. The only reason is that it is under the triple integral section. Thanks for the help.
Originally Posted by shawsend