### Home > CALC > Chapter 9 > Lesson 9.3.1 > Problem 9-80

9-80.

Write the integral that calculates the volume generated when the region bounded by

*y*=*x*^{2}and*x*=*y*^{4}is rotated: Homework Help ✎About the

*x*-axis.About the

*y*-axis.About the line

*x*= 2.

Sketch the region and determine the points of intersection.

The outside radius (*R*) is the curve *x* = *y*^{4}. The inside radius (*r*) is the curve *y* = *x*^{2}. 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*).