00:01
All right.
00:02
First, let's get us a reasonable picture of this.
00:05
Usually when i draw the sign of x, i just throw it on there.
00:09
But because we've got the sign of x and a thing that's not a trig function, got to be a little bit more careful.
00:17
Okay, so i'm going to have those be ones.
00:20
So one, two, three, so that we'll put pi about right here.
00:25
Okay, one, two.
00:29
Okay, halfway between zero and pi is pi over two.
00:34
We'll put that right there.
00:37
The sign starts at zero.
00:40
It's at 1 at pi over 2, and it's back to 0 at pi.
00:45
Okay, so it looks like that.
00:50
All right, y equals x goes through 0 -112.
00:56
1 -2 -2.
01:03
Oops, let's try again.
01:07
Oh, this picture's going to go create, whoops, let me try one more time.
01:10
Picture is going to go off the screen oh no no i'm going to get it all right only made a dye because i can draw them better i don't know why it doesn't make any sense but that's how it works for me okay x equals pi over two that's this vertical line x equals pie that's this vertical line see what i mean okay try one more time although i did draw the green one okay all right so do you see the area that you're trying to find above the blue line, which is the sign, in between these two black lines, and then beneath the green line? all right.
02:11
So it wants to know should you integrate vertically or horizontally to find the area.
02:19
Okay, so look at these horizontal slices that i'm drawing.
02:25
This one has the black line pie on the right hand side.
02:30
And the green line, y equals x, on the left hand side.
02:35
But now look at this one.
02:38
It has the black line on the right and pie over two on the left.
02:44
And then look at this one.
02:46
It has the black line on the right and the blue one on the left.
02:50
That means we have to do three integrals to find this because we have three different kinds of pieces...