CPM Homework Help : CALC Problem 9-80

Write the integral that calculates the volume generated when the region bounded by y = x² and x = y⁴ is rotated: Homework Help ✎
1. About the x-axis.
2. About the y-axis.
3. About the line x = 2.

Sketch the region and determine the points of intersection.

Hint (a):

The outside radius (R) is the curve x = y⁴. The inside radius (r) is the curve y = x². This will be a "dx" integral, so make sure your radii expressions are in terms of x.

Identify which curve will be the outside radius and which curve will be the inside radius. This will be a "dy" integral, so make sure your radii expressions are in terms of y.

Since x = 2 is a vertical line, this will be similar to part (b). This time the outside radius will be (2 – R) and the inside radius will be (2 – r).