### Home > PC3 > Chapter 13 > Lesson 13.2.1 > Problem13-61

13-61.

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 sub-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.

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