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9-80.
  1. 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.

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).