00:01
In this question we want to find the volume generated by this curve in the first quadrant with x equals to 1 and revolving about the x -sacist.
00:13
So e to power 2x will look like this.
00:17
This is 1 .0 over here.
00:20
Y equals e to power 2x.
00:23
We'll just take a small strip over here.
00:25
The width is so small is just delta x or dx.
00:29
And the y value here is just y.
00:33
So as it revolves around the x -assiz, you can see that it forms a small disk of height dx and radius y.
00:48
So the volume of this small disk is pi, r square will be y square, and the height is d x.
00:58
As we sum from 0 to 1, it is a continuous summation, so it is the integration sign, x from 0 to 1.
01:09
To 1 or the small disk between 0 to 1.
01:13
So pi y square d x.
01:15
So this will be our volume.
01:19
So volume is equals to 0 to 1 pi y square d x.
01:31
As pi is a constant, we can bring it outside the integral sign.
01:35
Y square is e to power 2x, e to power 2x d x.
01:41
There are a couple of methods we can use to indicate...