This document discusses several methods for approximating the area under a curve in calculus, including using rectangles with the right endpoint, left endpoint, and midpoint formulas to divide the area into sections and add them together. It also presents the power sums formula and works through an example problem of using the right endpoint rectangle approximation with N sections to find the area under a given curve and taking the limit as N approaches infinity.

1. Approximating and
Computing Area
AP Calculus
Section 5.1

2. Approximating using
Rectangles

3. Right Endpoint Formula
• Approximating the area under a curve using the
right endpoint approximation

4. Left Endpoint Formula
• Approximating the area under a curve using the left
endpoint approximation

5. Midpoint Formula
𝑏− 𝑎
Δ𝑥 =
𝑁

6. Power Sums

7. Example Problem
• Find a formula and compute the area under the
curve using RN and the limit as N approaches ∞ for
the function:

8. Example Problem

9. Example Problem

10. Example Problem

11. Example Problem