Let a Denote the Area Enclosed by the Graph $f ( x ) = \frac { \sqrt { x } } { 3 },$

Multiple Choice

Let A denote the area enclosed by the graph $f ( x ) = \frac { \sqrt { x } } { 3 },$ the x-axis, and the lines x = 0 and x = 9. Graphing the region and using plane geometry, we can find that A is

A) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \frac { 3 } { n } \sqrt { \frac { k - 1 } { n } }$
B) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \frac { 27 } { n } \sqrt { \frac { k } { n } }$
C) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \frac { 3 } { n } \sqrt { \frac { k } { n } }$
D) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \frac { 9 } { n } \sqrt { \frac { k - 1 } { n } }$
E) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \frac { 27 } { n } \sqrt { \frac { k - 1 } { n } }$