The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x^2 + 23x − 132, y = 0; about the y−axis

Question

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.

y = −x² + 23x − 132, y = 0;  about the y−axis

V=?

Answer 1

The roots of y are 11 and 12.

The answer is the integral from 11 to 12 of 2πy dx where y=-x²+23x-132.

The integral is quite easy to evaluate or you can get it on your graphing calculator.