### Home > APCALC > Chapter 10 > Lesson 10.2.2 > Problem10-124

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 $\lim\limits _ { n \rightarrow \infty } \displaystyle\sum _ { k = 1 } ^ { n } \frac { 5 } { n } \sqrt { 4 + \frac { 5 k } { n } }$.

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

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

$a = 4$

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