Let ​ Use a Riemann Sum with Four Subintervals

Multiple Choice

Let ​ Use a Riemann sum with four subintervals of equal length ( ) to approximate the area of R (under the graph of f on the interval [0, 2]) . Choose the representative points to be the left end points of the subintervals.
​
Repeat previous part with eight subintervals of equal length ( ) .
​
Compare the approximations obtained in previous parts with the exact area (14 sq units) . Do the approximations improve with larger n?
​

A) 12.25 sq units; 10.5 sq units; no
B) 10.5 sq units; 12.25 sq units; no
C) 10.5 sq units; 12.25 sq units; yes
D) 12.25 sq units; 10.5 sq units; yes