00:01
So here we're given a drawing of this function and asked to evaluate some integrals based on the fact that the area under the curve is equal to the integral.
00:11
So first, the integral from 0 to 16 is going to be the area of a rectangle, which has a base of 16 and a height of 8, plus the area of a triangle, which has a base of 16 and a height of 16.
00:26
So the area of the triangle is base times height over 2, and those two areas add up to 200.
00:31
Next, the area from 0 to 40 is going to be the area we just calculated, plus the remaining area from 16 to 40.
00:41
And first we have a rectangle with a width of 8 and a height of 24.
00:46
So i'll have 8 times 24.
00:48
And then we have a triangle with a base of 16 and a height of 24.
00:53
So that area would be 16 times 24 over 2.
00:57
And when you add that up, you get 640...