00:01
So here we're asked to prove with the exact value of this is going to be equal to 1 minus 2 over e.
00:05
So what we're going to do is let u be equal to x.
00:08
E equals x.
00:12
Bb equals e to the power of negative x d x and then just v is going to be equal negative e to the power of negative x.
00:24
Okay, so now we have all these.
00:27
So i'll write out what we originally started with, which was x, e to the power of negative x, dex, this is equal to negative x now negative x e to the power of negative x 1 .0 plus.
00:53
Okay.
00:54
So now this is equal to negative x, e to the power of negative x minus e to the power of negative x minus e to the power of negative x, which now we know is equal to 1 minus 2 over e.
01:17
So now we've proved how we get this exact value.
01:20
On the next page now i'm going to show how we use the midpoint rule to approximate.
01:23
So we know that change in x is going to be delta x is going to be to 1 over 16 because we have b minus a over n.
01:29
So that's going to be 1 minus 0, and then n is equal to 16.
01:32
So now our intervals are going to be 0, 1 over 16, and then we have 1 over 16, 2 over 16 or 1 8.
01:44
And we obviously would just keep doing this...