If the area under the curve of f(x) = x^2 + 2 from x = 1 to x = 6 is estimated using five approximating rectangles and right endpoints, will the estimate be an underestimate or overestimate? a. underestimate b. overestimate c. the area will be exact d. the area cannot be estimated with just five rectangles

(B) Overestimate

Step-by-step explanation:

This parabola is convex (open up) and the interval of estimation interrogates the curve in a range where the function is increasing.

If the rectangles match the function value with their upper-right corners, the upper rectangle side is never below the actual curve. This is true for all five (or any number of) rectangles in the interval. Therefore the estimated area will be strictly an overestimate.

false

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