00:01
All right, so what they want us to do in this problem is they want us to integrate.
00:06
So we've got to find the area under the curve from 7 to 12 on that interval.
00:12
So we're integrating.
00:15
So we're given the function there is the rate.
00:18
So when we integrate it, that's going to give us the production, how much we actually get.
00:25
Okay, so i broke it up into two different integrals.
00:29
So i'm going for the integral from 7 to 12 of 80 over t plus 8 times dt plus, and then for that 8, i just did a separate one from 7 to 12 of 8 dt, the change in the time.
00:45
Okay, so for the one on the left, i did like a u substitution.
00:50
I made u equal t plus 8, so d u equals dt.
00:56
I took that 80, brought it out in front of the integral.
01:00
Now you might be wondering like where did 15 and 20 come from? i changed my limits of integration.
01:07
So it reflects for you.
01:09
So i put 7 in for t, 7 plus 8 is 15, that's where, so u is going to go from now 15 to 20, 12 plus 8 is 20, instead of going from 7 to 12...