evaluate triple integral of z.dV where the solid E is bounded by the cylinder y2+z2=9 and the planes x=0 and y=3x and z=0 in the first octant
for cylindrical polar co-ords, x=rcos[tex]\theta[/tex], y=rsin[tex]\theta[/tex] and z=z
The Attempt at a Solution
im just struggling to grasp the bounds here. the cylinder has x as its centre line. and r=3. which means shape extends out from x 3 units along y and z axis's. and extends along x from origin 3x units. then stops due to plane on y. thats about as much as i can gather. the projected region that i should take the volume of the solid over should be projected onto the yz plane for this case. which would show a quarter circle with r = 3 right? with y=sqrt(9-z2) with y>0 so achieve first quadrant.
but i cant actually work out what to integrate each integral between.
help? much appreciated!