Use the following information to answer questions 32-34.

The curve y = 0.005x2 - 2x + 200 for 0 ≤ x ≤ 200 and the line segment from F(0,200) to G(200,0) are shown in the standard (x, y) coordinate plane below.

34. Tran wants to approximate the area underneath the curve y = 0.005x2 - 2x + 200 for 0 ≤ x ≤ 200, shown shaded in the graph below.

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

Answer and Explanation

Your Answer is

Correct Answer is F

Explanation

According to the information in the figure, the shaded area is the integral of the parabola, and the area under the FG line segment is the integral of the straight line. Since the parabola is lower than the straight line in the range from 0 to 200, the integral (area) is also smaller than the straight line, so the answer is F.

The shaded area can also be regarded as the area under the straight line minus the area of ​​the arc (the area between the intersection points of the straight line and the parabola), then the shaded area must be smaller than the area of ​​the straight line.