00:01
We have a cistern that is getting filled.
00:04
The cistern can hold up to 2 ,000 liters and it starts empty.
00:09
We're also given the rate of change, the q prime of t, that the water is coming in.
00:16
First, we want to know how much water has flowed in in an hour or 60 minutes.
00:24
Well, if we integrate the rate of change, that will give us the amount that's flowed in.
00:37
So i'm going to have q of 60 equals the integral from zero to 60 of my q prime.
00:46
Let's separate this into two columns.
00:49
The integral of that would be, well, that's three to the one -half power.
00:57
And if you add one to the power, that's going to be the three -half power.
01:05
And then i'm going to divide by three - halves or multiply by two -thirds, and three times two -thirds is two.
01:17
Evaluated from zero to 60.
01:20
If i fill in 60, i will get about 929 .5 liters.
01:33
And i would subtract what i get when i fill in zero, but that's zero.
01:38
Now, i did start empty.
01:41
So if it went up by 929 .5 liters, that is its new amount of water in it.
01:52
Next, we want to feel...