Integrate the function f(xyz)=−4x+6y over the solid given by the "slice" of an ice-cream cone in the first octant bounded by the planes x=0 and y=x*sqrt(22/3) and contained in a sphere centered at the origin with radius 13 and a cone opening upwards from the origin with top radius 5.
The Attempt at a Solution
So I changed function 6y-4x into the terms of spherical coordinates. While i attempted to find the limits of the integral, I'm not sure if my drawing is correct:
But I assumed it meant that the region had to be inside the cone such that it was in the first octet (since it's bounded by x=0 which is the yz plane --NOT SHOWN IN PICTURE), but I'm not sure how the ice cream part has to do with this...
Could someone just explain to me what the trace part means and also explain if my drawing is right, I have no idea what inside the circle and the cone means..