00:01
Here we're given a function graphically and we want to find what is the integral of it over certain regions.
00:05
So let's say we have the integral from 0 to 2 of f of x dx.
00:08
That means i want to take from 0 to 2 this whole area here.
00:13
So i'm going to break that up and say well that's an area of 4 for that square and an area of 2 for that.
00:19
So that's just 4 plus 2 is 6.
00:21
If i want the integral from 0 to 5, well 1, 2, 3, 4, 5.
00:27
So that's going to go up to here.
00:29
So now i need to calculate this area here.
00:32
So what i'm going to do is i'm going to say i have 1, 2, 3, 4.
00:35
And then this whole region to 6 here is going to be a triangle of 1, 2, 3 by 1, 2, 3, 4.
00:44
3 times 4 is 12, 6.
00:45
So that has an area of 6...