CPM Homework Help : CALC Problem 4-45

Use a Riemann sum with $20$ rectangles to approximate the following integrals. Then use the numerical integration feature of your graphing calculator to check your answer.

Hint:

General form of left-endpoint Riemann sum:
$\displaystyle \sum_{i=0}^{n-1}\Delta xf(a+\Delta xi)$

$\int _ { 0 } ^ { 4 } ( 2 - 4 x ^ { 3 / 2 } ) d x$
Hint (a):
Riemann approximation:
$\approx \displaystyle\sum_{i\rightarrow 0}^{19}\frac{1}{5}f\left ( 0+\frac{i}{5} \right )=\sum_{i\rightarrow 0}^{19}\frac{1}{5}\left ( 2-4\left ( \frac{i}{5} \right )^{\frac{3}{2}} \right )=-40.04$
Your calculator should reveal that
$\int_{0}^{4}\left ( 2-4x^{\frac{3}{2}} \right )=-43.2.$

$\int _ { 1 } ^ { 8 } \sqrt { 4 x + 3 } d x$
Hint (b):
Refer to part (a).