Question

use cylindrical coordinates. evaluate e z dv, where e is enclosed by the paraboloid z = x2 y2 and the plane z = 16.

Answer 1

To evaluate e^zdv using cylindrical coordinates, substitute x = rcos(theta) and y = rsin(theta) to convert the integral. The limits of integration are determined by the given surfaces: the paraboloid z = x² y²and the plane z = 16.

Step-by-step explanation:

To evaluate ezdv using cylindrical coordinates, we need to determine the limits of integration and the volume element in cylindrical coordinates. The limits of integration are determined by the given surfaces: the paraboloid z = x2y2 and the plane z = 16.

To convert the integral to cylindrical coordinates, we substitute x = rcos(theta) and y = rsin(theta). The volume element in cylindrical coordinates is dv = r dz dr d(theta) .

Substituting the limits of integration and the volume element, the integral becomes: ezdv = ∫02π ∫0r ∫016 ez r dz dr d(theta).