Let and compute the Riemann sum of f over the interval , using
Two subintervals of equal length ( ).

Five subintervals of equal length ( ).

Ten subintervals of equal length ( ).

In each case, choose the representative points to be the right end points of the subintervals.

A) 79.52 sq units; 84.48 sq units; 100 sq units;
B) 84.48 sq units; 79.52 sq units; 100 sq units;
C) 100 sq units; 84.48 sq units; 79.52 sq units;
D) 100 sq units; 79.52 sq units; 84.48 sq units;

Question

Let  and compute the Riemann sum of f over the interval  , using ​
Two subintervals of equal length (  ).
​
Five subintervals of equal length (  ).
​
Ten subintervals of equal length (  ).
​
In each case, choose the representative points to be the right end points of the subintervals.
​
A) 79.52 sq units; 84.48 sq units; 100 sq units; 
B) 84.48 sq units; 79.52 sq units; 100 sq units; 
C) 100 sq units; 84.48 sq units; 79.52 sq units; 
D) 100 sq units; 79.52 sq units; 84.48 sq units;

Quizplus · Accepted Answer

We can calculate the Riemann sum using the right-endpoint rule:

For two subintervals of equal length:
Δx = (33.95 - 20.95)/2 = 6
f(26.95)*6 + f(32.95)*6 = 79.52

For five subintervals of equal length:
Δx = (33.95 - 20.95)/5 = 2
f(22.95)*2 + f(24.95)*2 + f(26.95)*2 + f(28.95)*2 + f(30.95)*2 = 84.48

For ten subintervals of equal length:
Δx = (33.95 - 20.95)/10 = 1.3
f(22.25)*1.3 + f(23.55)*1.3 + ... + f(32.25)*1.3 = 100

Therefore, the answer is C: 100 sq units; 84.48 sq units; 79.52 sq units; as the Riemann sum gets closer to the actual area as the number of subintervals increases.

Let and Compute the Riemann Sum of F Over