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

Question

Quizplus · Accepted Answer

Using right endpoints, the width of each rectangle is $\Delta x = \frac{5-0}{5} = 1$. The heights of the rectangles are: $f(1) = 48$, $f(2) = 45$, $f(3) = 40$, $f(4) = 33$, and $f(5) = 24$. Thus, the area approximated by the rectangles is:
$$A \approx f(1) \cdot \Delta x + f(2) \cdot \Delta x + f(3) \cdot \Delta x + f(4) \cdot \Delta x + f(5) \cdot \Delta x$$$$=48\cdot1+45\cdot1+40\cdot1+33\cdot1+24\cdot1=190$$
Therefore, the answer 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 $f ( x ) = 49 - x ^ { 2 }$