CPM Homework Help : APCALC Problem 10-124

Determine the integral that is being approximated with the Riemann sum $\displaystyle\sum _ { k = 1 } ^ { n } \frac { 5 } { n } \sqrt { 4 + \frac { 5 k } { n } }$ . Then, calculate the value of $\lim\limits _ { n \rightarrow \infty } \displaystyle\sum _ { k = 1 } ^ { n } \frac { 5 } { n } \sqrt { 4 + \frac { 5 k } { n } }$ .

Hint:

$\displaystyle\sum_{k=1}^nf(a+k\Delta x)(\Delta x)=\int_a^bf(x)dx$

More Help:

$\Delta x=\frac{b-a}{n}$

Step:

$a = 4$

$\Delta x=\frac{b-a}{n}=\frac{b-4}{n}=\frac{5}{n}$