00:01
In order to find the area between two curves, we need to find the integral from the intersection points or the boundary points of the function that is on top minus the function that is on the bottom.
00:19
We take that, apply the parameter for the element displacement.
00:27
It could be x, it could be y, it doesn't really matter, but in this case it will be x.
00:32
So our functions, the top function if we look at the graph, f top will be equal to e to the x.
00:43
F bottom will be equal to x e to the x.
00:52
Now we see that there is an intersection point at x equals 1, y equals e, but we're bounded by the line x equals 0 for both of these.
01:01
So we are bounded by the line x equals 0 and the line x equals 1 we could say.
01:14
So that's the region we're going to take the area in.
01:17
So we'll just apply the area formula.
01:19
Now for us that will be the integral from 0 to 1 of the top function e to the x minus the bottom one, e to the 2x, squared actually.
01:34
Original problem, x e to the x squared.
01:37
That doesn't make it too much more difficult, actually if it was x e to the x it would be a lot more complicated so this makes it better for us.
01:45
Now these are two integrals, i can do them separately, right? so the integral from 0 to 1 of e to the x dx minus the integral from 0 to 1 of e to the squared dx...