00:01
In this question, they say the rate at which cars enter a parking lot is modeled by e of t, while the rate at which cars leave the parking lot is modeled by the differential function l.
00:14
Selected values of l of t are given in the table above.
00:18
Both e of t and l of t are measured in cars per hour, and time t is measured in hours after 5 a .m.
00:25
The functions are defined for times 0 through 12.
00:29
In part c of this question, i want to use a trapezoidal sum with the four sub -intervals indicated by the data in the table to approximate the integral from 2 to 12 of l of t dt.
00:43
Using correct units, we're going to explain the meaning of the integral from 2 to 12 of l of t dt dt in the context of this problem.
00:56
So let's see.
00:57
I am considering the integral from 2 to 12 of l of t dt.
01:07
So what would i say? the area of a trapezoid is one half the height times the sum of the bases.
01:15
So i'm going to have four trapezoids here.
01:19
My first trapezoid has a height of 3.
01:22
We're we're going from t equals 2 to t equals 5, while the bases are 15 and 40.
01:29
To this, i add the area of the second trapezoid.
01:33
Half the height, the height of that second trapezoid, is the distance from t equals 5 to t equals 9, which is 4, times the sum of the bases, which is 40 plus 24.
01:47
To this, i add half the height.
01:51
The height of that third trapezoid is 2.
01:54
I'm going to multiply by the sum of the bases...