### Home > APCALC > Chapter 4 > Lesson 4.1.1 > Problem4-9

4-9.

Write a Riemann sum that approximates the area under the curve for $–8 ≤ x ≤ 8$ using the given number of rectangles if $f\left(x\right) = 2x^{1/3} + 1$. Then evaluate the sum with a calculator.

1. $16$ rectangles

Let's use right endpoint rectangles:

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

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

2. $64$ rectangles

Let's use midpoint rectangles:

$\sum_{i=1}^{n-1}\Delta xf\left(a+\frac{\Delta x}{2}i\right)$