00:01
So in this problem, we need to estimate the distance a car traveled while breaking over a six second interval.
00:05
And all we have is this graph of its velocity.
00:08
We know that the area under a velocity curves equal to its definite integral over that interval, which is equal to distance traveled.
00:15
So we need to figure out the area between this curve and the x axis.
00:19
Unfortunately, we don't have an equation for this curve, so we can't precisely calculate the area.
00:24
But what we can do is make an estimate using intervals.
00:27
The first thing we have to do is choose our interval length, so i'm going to use one, which means we'll have six intervals one every second along the x axis.
00:35
Now, looking at this graph, i'm gonna find the velocity at each second from 0 to 6 and put those in this table.
00:41
We make our estimates by pretending the velocity is constant over each one.
00:45
Second interval, even though it really isn't, we can do this using left intervals or right intervals using left intervals looks like this.
00:52
Each rectangle covers one interval, and its height is determined by the velocity at the start of that interval.
00:58
This allows us to easily estimate the area under the curve by adding up the area of the rectangles...