CPM Homework Help : APCALC Problem 8-91

Multiple Choice: The expression $\frac { 1 } { 20 } [ ( \frac { 1 } { 20 } ) ^ { 2 } + ( \frac { 2 } { 20 } ) ^ { 2 } + ( \frac { 3 } { 20 } ) ^ { 2 } + \ldots + ( \frac { 20 } { 20 } ) ^ { 2 } ]$ is a Riemann sum approximation of:

$\int _ { 0 } ^ { 1 } x ^ { 2 } d x$

$\frac { 1 } { 20 } \int _ { 0 } ^ { 1 } x ^ { 2 } d x$

$\frac { 1 } { 20 } \int _ { 0 } ^ { 1 } ( \frac { x } { 20 } ) ^ { 2 } d x$

$\int _ { 0 } ^ { 1 } ( \frac { x } { 20 } ) ^ { 2 } d x$

$\frac { 1 } { 20 } \int _ { 1 } ^ { 20 } ( \frac { x } { 20 } ) ^ { 2 } d x$

Hint:

$\lim\limits_{\text{base}\rightarrow 0}\displaystyle\sum_{\text{rectangle}(a)}^{\text{rectangle}(n)}(\text{base})(\text{height})=\lim\limits_{\Delta x\rightarrow 0}\sum_{i=1}^{n}\Delta x(f(a+\Delta xi))=\lim_{n\rightarrow \infty }\sum_{i=1}^{n}\frac{1}{n}f\left ( a+\frac{i}{n} \right )=\int_{a}^{b}f(x)dx$