00:01
Since this problem starts at zero and they ask for increments at three, four, up to six, i could go to eight, but i might just go all the way to ten.
00:18
What i have to acknowledge first is the area from zero to three, and when you're below the x -axis you're going to get a negative area, but when you're above you'll be a positive.
00:28
So what i'm going to do is just acknowledge that this little rectangle here would be one by three rectangles, so it's three, but i'm gonna write down that's a negative.
00:37
And then this triangle i'm drawing is a base of three with a height of one, so that's negative three halves.
00:48
And then this triangle, i'll just draw it again, is one half times one with a height of two, so that area one half of two would be one, but again it's below the x -axis.
01:03
And then from four to six, that area above the x -axis, so it's positive now, is a triangle.
01:11
So one half times the base of two with a height of four, so half of two is one times four.
01:18
And then you just have a rectangle going from six to eight, and it's a two by four, so that area would be eight.
01:26
And then you have another triangle on top of a rectangle, and the rectangle has an area of two.
01:33
Just double check my math.
01:35
So when they ask you to do, first of all, you can move that five in front.
01:40
I think that's just there to mess with you.
01:42
F of x dx.
01:45
So all you have to do is that five is still there, but multiply by the area from four to six, which was four, and so your answer is 20.
01:54
And then the same thing for the next one, they put a five in there, i think again to confuse you, but now you're doing from zero to three where we had a negative area...