Estimate the area from 0 to 5 under the graph of $f(x)=25-x^{2}$ using five approximating rectangles and right endpoints.
A) $65$
B) $60$
C) $170$
D) $270$
E) $70$

Question

Quizplus · Accepted Answer

To estimate the area under the curve using right endpoints, divide the interval [0, 5] into 5 equal subintervals of width 1. The right endpoints are x = 1, 2, 3, 4, 5. Evaluate f(x) at these points: f(1) = 24, f(2) = 21, f(3) = 16, f(4) = 9, f(5) = 0. The sum of the areas of the rectangles is 24 + 21 + 16 + 9 + 0 = 70.

Estimate the Area from 0 to 5 Under the Graph f(x)=25−x2f(x)=25-x^{2}f(x)=25−x2

Estimate the Area from 0 to 5 Under the Graph $f(x)=25-x^{2}$