CPM Homework Help : CALC Problem 1-121

WHICH IS BETTER? Part Two
Below is a comparison between using rectangles and trapezoids to approximate the same area under a curve for $f(x)$ . Decide which method you think will best approximate $A(f, a ≤ x ≤ b)$ . Then approximate each area if $f(x) = -0.25x(x - 9)$ , $a = 2$ , and $b = 8$ using $3$ sections. Compare your results with the actual area $A = 25.5$ square units.

Midpoint Rectangles

Trapezoids

Hint 1:

Which method comes closer to the actual curve $f(x)$ ?

Hint 2:

Each section is $2$ units wide. Use this knowledge and the equation of the function to find the areas of each section for both methods.

Hint 3:

Which method gave you the number closest to $25.5$ ?