Use a finite approximation to estimate the area under the graph of the given function on the stated interval as
instructed.
-$$f ( x ) = x ^ { 2 } \text { between } x = 0 \text { and } x = 1 \text { using a lower sum with two rectangles of equal width. }$$
A) .75
B) .625
C) .125
D) .3145

Question

Quizplus · Accepted Answer

To estimate the area using a lower sum with two rectangles, divide the interval [0,1] into two equal subintervals: [0,0.5] and [0.5,1]. The width of each rectangle is 0.5. The height of each rectangle is determined by the function value at the left endpoint of each subinterval. For [0,0.5], the height is f(0) = 0^2 = 0. For [0.5,1], the height is f(0.5) = (0.5)^2 = 0.25. The area is (0.5)(0) + (0.5)(0.25) = 0.125.

Use a Finite Approximation to Estimate the Area Under the Graph