In this section on application of integration to volume, you’ll find the formula used to find the volume generated when a curve is rotated about the x-axis and y-axis.

## Formula for finding volume generated

To find the volume generated by a region R, bounded by the curve y = f(x), the x-axis, the lines x= a and x= b, when it is rotated completely about the x-axis:

To find the volume generated by a region R, bounded by the curve x = g(y), the y-axis, the lines y= a and y= b, when it is rotated completely about the x-axis: