Evaluate the following integrals

For question no.1: label all important points such as intercepts, vertices of parabolas and hyperbolas, endpoints of the major and minor axes of ellipses, and endpoints of traces.

Consider the parabola E : x = z2 4 in the rz-plane. 1. Sketch the portion of the graph of the cylinder whose equation is the same as E in between the xz-plane and the plane y = 4. 2. Give an equation for the surface of revolution generated when E is revolved about the x-axis.