00:01
For this problem, we are to determine the values of the following integral.
00:04
So the first one, we have integral from 0 to 2 of f of x, dx.
00:08
This is the area of the region that's bounded by f of x, and the x, x, is, on the closed interval 0 to 2.
00:16
So it should be this region.
00:18
And that's the area of a trapezoid, which is equal to 1ā2, times upper base, let's call it b sub 1, plus the lower base, b sub 2.
00:30
Times the height h, that'll be one half of, say this is b sub 1, this is b sub 2, and this is our h, that will be 1 plus 3 times a height of 2.
00:46
This is equal to 4.
00:48
Next we have the integral from 0 to 5 of f of x, dx, that's the area of the region bounded by f, and the x -x is on the closed interval of 0 to 5.
00:58
So this is the same as integral from 0 to 2, f of x, dx, plus integral from 2 to 5 f of x dx.
01:09
So since you already have integral from 0 to 2 of f, that's 4 plus, we'll have the area of the region on the closed interval 2 to 5, which is this area...