The curve `y = 0.005x^(2) - 2x + 200` for `0 le x le 200` and the line segment from `F(0.200)` to `G(200,0)` are shown in the standard (x,y) coordinate plane below.

Tran wants to approximate the area underneath the curve `y = 0.005 x^(2) - 2x + 200` for `0 le x le 200`, shown shaded in the graph below.

He finds an initial estimate, A, for the shaded area by using `bar(FG)` and computing `A = 1/2(200 units) (200 units) = 20,000` square units.
The area of the shaded region is:

Options

A. less than 20,000 square units, because the curve lies under `bar(FG)`.
B. less than 20,000 square units, because the curve lies over `bar(FG)`.
C. equal to 20,000 square units.
D. greater than 20,000 square units, because the curve lies under `bar(FG)`.

Answer

A