00:01
So you have the graph of f of t, and let me just quick sketch that.
00:06
This goes up to 4, and this goes down to negative 2.
00:12
And we have it 1, 2, 3, 4, 5, 6, 7.
00:20
And our graph starts here.
00:22
Let me do that in.
00:23
Let me do it in red.
00:24
And so this is f of t.
00:25
It starts here, goes to here, and then it goes up to here, and goes all the way down to zero.
00:36
And then right here is at 5.
00:40
And this drops down.
00:43
It's like doing that.
00:45
And it's a straight line slope of negative 1 there.
00:48
And then it stays constant until you get to 6.
00:51
You hear the ring doorbell, don't you? and then it goes up.
00:55
And again, this is f of t.
00:57
This is the f function and this is the t variable.
00:59
And we have the function g of x that is the accumulation function starting at zero, going to x of f of t, d t.
01:13
And so we want to find these functional values.
01:16
And i basically, i'll make a little table here of values, and this will be x, and this will be g of x.
01:24
And we go from zero to one, to two, to three.
01:28
And they ask for all those.
01:30
They don't ask for four, and they ask for five, i believe.
01:34
They don't ask for six.
01:36
Or maybe they do ask for six.
01:37
But in any case, let's just fill in this chart.
01:40
And so we are accumulating, and we're starting here.
01:44
And so the area from zero to zero is zero.
01:47
The area from zero to one is two units.
01:52
The area from zero to two, and we find the area of this component, and we can see that from here to here that this is two, and then we have a triangle here that's one by two, and so this area is one here, so one, two, three.
02:11
So i add on three units to what we previously had, and we're up to five.
02:16
So we add on three.
02:18
So from one to two is adding on three more units.
02:21
And now we continue on.
02:23
From two to three, we want to add that accumulative area on.
02:27
So we keep accumulating from zero.
02:30
And this is 1 by 4.
02:32
So the area this triangle is 2.
02:34
So we accumulate and add on 2 to what we previously had.
02:37
So we're up to 7.
02:39
And now we start to go negative...