Integrate the function f(x,y,z)=−7x+2y over the solid given by the "slice" of an ice-cream cone in the first octant bounded by the planes x=0 and y=sqrt(263/137)x and contained in a sphere centered at the origin with radius 25 and a cone opening upwards from the origin with top radius 20. I am not sure I am getting the right picture. Here are the bounds for the integral I found. arctan(sqrt(263/137)) <= theta <= pi/2 0 <= z < 15 0 <= r <= (4/3)z I am integrating in the order of dr dz d_theta. The integrand I cam up with is... -7r2 * cos(theta) + 2r2 * sin(theta) dr dz d_theta Can anyone tell me where I went wrong. I keep getting a crazy answer.