00:03
All right, we're asked to find the area between y equals e to the x and y equals x on the interval from 0 to 1.
00:10
Just to get a quick sketch of this, you should know what y equals e to the x looks like.
00:15
That is an exponential function.
00:17
We know it's going to cross at the point 0, 1, right? because e to the 0, anything to a power of 0 would be 1 other than 0 to the 0.
00:27
And then y -equaling x is just this function down here.
00:31
Y equaling x looks like this.
00:33
And so there's no problem of which function is the top function, which one is the bottom.
00:37
We just want to find the area between these two on the interval from zero until one.
00:44
So hopefully you know your formula for area between curves with calculus.
00:48
Our area is equal to the integral from a to b, so zero to one, of the top function minus the bottom function.
00:55
Well, it's easy as c.
00:56
In this case, it's e to the x is the top function, minus x is the bottom function.
01:02
All right.
01:03
We need to integrate e to the x.
01:05
Well, that's a nice one...