### Home > PC > Chapter 2 > Lesson 2.3.5 > Problem2-127

2-127.

Write down the sums (but DO NOT add them up) that you would use to approximate $A(2^x,1\le x\le4)$ using six intervals and:

$\text{rectangle width }=\frac{\text{length of interval}}{\text{# of sub-intervals}}$

1. Left endpoint rectangles.

This sum should start at $n = 0$ and end at $n = 5$.

2. Right endpoint rectangles.

This sum should start at $n = 1$ and end at $n = 6$.

3. Trapezoids.

Draw all of the trapezoids. Then calculate the area for each.

$\text{area }=\text{width}\cdot \frac{(\text{base}_{1}+\text{base}_{2})}{2}\text{ for each trapezoid}$