### Home > APCALC > Chapter 3 > Lesson 3.3.3 > Problem3-116

3-116.

For each function below, write and evaluate a Riemann sum to calculate the area under the curve for $–2 ≤ x ≤ 1$ using $24$ left endpoint rectangles. Homework Help ✎

General form of a left-endpoint Riemann sum:

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

1. $f(x) = 2^x$

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

where $a$ and $b$ are the starting and ending values and $n$ is the number of rectangles.

1. $f ( x ) = \sqrt { x + 2 }$

Refer to the hints in part (a).