CPM Homework Help : APCALC Problem 3-177

Write a Riemann sum to estimate the area under the curve for $0 ≤ x ≤ 2$ using $n$ left endpoint rectangles given $g(x) = −x^2 + 4$ .

Answer:

General left-endpoint Riemann sum:

$\displaystyle \sum_{i=0}^{n-1}\Delta xf(a+\Delta xi)$

$g(x)\approx \displaystyle \sum_{i=0}^{n-1}\frac{2}{n}\left ( a+\frac{2i}{n} \right )$

Calculate the sum for $n = 20$ .
Hint (a):
Substitute.
How can you use your result to estimate the area under the curve for $−2\le x\le0$ ? What about the area under the curve for $−2\le x\le2$ ?
Hint (b):
Consider the shape of the graph of $g(x)$ .