00:01
All right, we have a fun inner girl to solve.
00:05
We could solve it by integration by parts, but this is a perfect one to instead use tabular, tabular integration.
00:14
Tabular integration.
00:16
So the way it works is you put the function whose derivative would become zero eventually on the left, and then we go ahead and take its derivatives.
00:26
A derivative of y is one, and then we get zero.
00:30
Then the other function has to be one.
00:32
We can take antiderivatives.
00:34
So we will take the anti -derivative, which will look like itself, divided by chain roll, so divided by 0 .2.
00:44
And then i'll take the anti -derivative one more time.
00:47
I will get e to the 0 .2.
00:50
Divided by 0 .2 again, so 0 .2 squared.
00:54
And i can clean this up.
00:57
This, by the way, is probably easier if i divide by a fifth.
01:01
It's really five e to the 0 .2 .y.
01:04
It's a little bit nicer to read.
01:06
And this then is 5 squared or 25, e to 0 .2.
01:11
All right.
01:12
So tabular integration, you do diagonals.
01:15
This first one's plus.
01:17
The second one's minus.
01:18
So our integral then equals y times 5e to 0 .2y, minus 25 e to 0 .2 .y...