### Home > APCALC > Chapter 3 > Lesson 3.4.3 > Problem3-177

3-177.

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

General left-endpoint Riemann sum:

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

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

1. Calculate the sum for $n = 20$.

Substitute.

2. 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 $−2\le x\le2$?

Consider the shape of the graph of $g(x)$.