Evaluate the triple integral of the region E, where E is the solid w/i the cylinder x^2+y^2=1, above the plane z=0, and below the cone z^2=x^2+y^2.
So is the plane z=0 same as the xy-plane? I was doing a hw problem that has
I just need help conceptually understand the limits of integration. So we know that x has intercepts at ±1 and y has intercepts at ±1. And since the cylinder lies along the z-axis, the radius integrand ranges from -1 to 1. The theta integrand ranges from 0 to 2∏. And the z integrand ranges from 0 to 2r.
Now when I saw the solution, it said that the radius integrand ranges from 0 to 1; not -1 to 1. Which makes me question, is the plane z=0 a vertical plane or horizontal plane? Or do you think the solution has an error? Because if the plane was vertical, the radius integrand would range from 0 to ∏