Question

Use a triple integral to find the volume of the wedge bounded by the parabolic cylinder y=x² and the planes z=17-y and z=0

Answer 1

To find the volume of the wedge bounded by the parabolic cylinder y=x² and the planes z=17-y and z=0, we can use a triple integral.

Step-by-step explanation:

To find the volume of the wedge bounded by the parabolic cylinder y=x² and the planes z=17-y and z=0, we can use a triple integral. The limits of integration for x, y, and z can be set as follows:

x: 0 to sqrt(y)

y: 0 to 17

z: 0 to 17-y

The integrand is 1, representing the infinitesimal volume element. The triple integral becomes:

∫∫∫ 1 dz dy dx

Integrating with respect to z, y, and x in that order gives the volume of the wedge.