Question

∬d³x2y da, where D is the top half of the disk with center the origin and radius 2.

A) Triple Integration
B) Disk Area Calculation
C) Surface Integral Computation
D) Volume Integration

Answer 1

To evaluate the given integral over the top half of the disk, we need to use triple integration with appropriate limits.

Step-by-step explanation:

To evaluate the integral ∬d³x2y da over the top half of a disk with center at the origin and radius 2, we can use triple integration.

First, we need to set up the limits of integration. Since the disk is the region above the xy-plane, the limits for z will be from 0 to the upper hemisphere of the disk. For the other two variables, x and y, since the disk has a radius of 2, the limits for x and y will be from -2 to 2.

Our triple integral becomes:

∫-22 ∫-22 ∫0√(4 - x² - y²) 2y dz dy dx