00:01
So in this question, they say that the graph of a function f is shown, we're going to evaluate each integral by interpreting it in terms of areas.
00:09
And it seems like you're very much on the right track here, but the major thing you forgot is the area below the x -axis is counted as negative by the definite interval, not positive.
00:23
So in a, when you had the integral from 0 to 16 of f -fx -d -x -d -x, you need to define the area of this trapezoid.
00:33
And the area of a trapezoid is one -half the height times the sum of the bases.
00:40
The height of this trapezoid is 16, and the bases, they were 8 and 24.
00:49
If you go to a calculator, one -half times 16 times the quantity of 8 plus 24 gives you the 256.
01:00
Units of area that are here.
01:03
Then from 16 to 24, well you have a rectangle.
01:09
That rectangle is 8 along the base and then 24 in terms of the height, 8 times 24 gives you 192.
01:23
So you have 192 here.
01:26
Then you have the triangle that extends over to x equals 40 right now the area of that triangle what's that it's one half times the base which is 16 times the height which is 24 so one half one half times 16 times 24, that gives you 192 as well.
01:59
So here, 192.
02:03
Then the piece of area that extends from x equals 40 to x equals 56, well, the area of that is again one -half times base times height.
02:16
But since that area lies below the x -axis, that's counted as negative by the definite interval.
02:23
So that's negative 192.
02:27
And so this piece here, we should be getting negative 192 for my integral from 40 to 56...