00:01
The way i'm reading this problem is that we have y equals e to the x, and then we are bounded by the y -axis, the x -axis, and the line x -equals 2, and we are revolving around the y -axis.
00:21
And they tell you to get your answer however you see fit.
00:25
So i'm just going to do the shell method because if you see i made a cylinder there, in the lateral area of a cylinder.
00:34
Is just 2 pi r h.
00:36
So the volume of this would be 2 pi.
00:40
The integral would go from 0 to 2 because it's the y -axis and the x -axis.
00:45
The radius of each one of these cylinders, because there's an infinite number of cylinders, would be x.
00:52
And the height of each one of these is e to the x, dx.
00:56
Now, i'm guessing because they let you use a calculator that you can just type that in and get the answer.
01:01
Let me just do that real quick.
01:02
So 2 pi the integral from 0 to 2 of x, e to the x, d x, and i get an answer of 52 .710.
01:22
Let me circle that, but let's actually show you how you can do this, is you can do not just u substitution, is integration by parts, because if you do u prime the derivative of x is d x and then v is just e to the x and then as you piece this together sorry if that notation doesn't make any sense to you it's just how i learned it is it's x e to the x minus the integral is still from zero to two of e to the x d x and then you can take the integral again and you have to do each piece from zero to two or still a two or two pie in front and you have to plug in these bounds.
02:13
So basically what i have is 2e squared minus e squared...