# How do you find the volume of the solid obtained by rotating the region bounded by the curves #y=2x^2+5#, and #y=x+3# and the y-axis, and #x=3# rotated around the x axis?

##### 1 Answer

Jun 21, 2015

Use disks/washers.

#### Explanation:

Sketch the region. Note that

Therefore:

At a particular

The volume of each representative disk would be

The volume of the washer is the difference, or

# = pi int_0^3 (4x^4+19x^2-6x+16) dx#

You can finish the integral to get