00:01
All right, let's first have a look at what this graph looks like, or the area here.
00:06
1, 0 minus 1.
00:08
So you get e to the minus 2, e to the 0, which is 1, and e to the 2.
00:19
Okay, so e to the minus 2, that's little 1, e squared, that's big.
00:25
Okay, so it's an exponential function that's decreasing.
00:30
Y equals 0, that's the x -axis.
00:33
X equals 0 that's the y axis x equals the ln of 3 somewhere right here let's put it all right we're going to send it around the x axis so let's just cut vertically and then we just make a little disk okay volume of a disk pi r squared h so h is the height of the disc the little blue part i drew which is really just the thickness of the slice.
01:17
So h is dx.
01:20
Then r is the radius from the axis of rotation up in this case.
01:26
So that's just y on the top minus y on the bottom.
01:31
Y on the top eats the minus 2x.
01:34
Y in the bottom is 0.
01:37
So each the minus 2x.
01:40
So the volume is pi.
01:43
Add up all the disks are squared h and then we're going to pile those disk up from here x equals zero to x equals ln3 all right so volume is pi zero to ln3 e to the minus two x squared how much is that what if i had x to the third and i squared it or you have x to the sixth right so if i have i have e to the minus 2x and i square it.
02:26
I use the same rule, which is multiply the exponent.
02:29
So e to the minus 4x, dx.
02:36
I'm going to let u be minus 4x...