Estimate the area from 0 to 5 under the graph of $f ( x ) = 49 - x ^ { 2 }$ using five approximating rectangles and right endpoints.
A) 191
B) 188
C) 190
D) 189
E) 192

Question

Quizplus · Accepted Answer

We have a base length of Δx = 1 since we are dividing the interval from 0 to 5 into 5 equally spaced intervals. 
Using right endpoints, our heights would be f(1), f(2), f(3), f(4), and f(5).
∴ Area ≈ f(1)Δx + f(2)Δx + f(3)Δx + f(4)Δx + f(5)Δx
≈ [49-(1)^2] + [49-(2)^2] + [49-(3)^2] + [49-(4)^2] + [49-(5)^2]
≈ 48 + 45 + 40 + 33 + 24
≈ 190
Therefore, the best choice is C).

Estimate the Area from 0 to 5 Under the Graph f(x)=49−x2f ( x ) = 49 - x ^ { 2 }f(x)=49−x2

Estimate the Area from 0 to 5 Under the Graph $f ( x ) = 49 - x ^ { 2 }$