00:01
We are asked to find the volume of the solid obtained by rotating the given region around the x -axis.
00:07
First, we'll sketch the region.
00:13
So, the region is bounded by the line y equals 2x, by the line x equals 3, and the x -axis.
00:22
So, this is the region, and we are asked to rotate this region around the x -axis.
00:29
So, on the next picture, i'll draw the solid that we'll get after rotation.
00:33
The solid we'll get is a cone.
00:55
So this will be the solid that we'll get.
00:58
And we are asked to find the volume of the solid.
01:01
We'll use the method of disks and washers.
01:14
By that method, the volume is the integral of pi multiplied by r squared, r capital squared minus r small squared dx from a to b.
01:28
A and b are the beginning and end points of the region...