This document discusses several methods for approximating the area under a curve, including using rectangles with right endpoints, left endpoints, and midpoints. It provides formulas for the right endpoint, left endpoint, and midpoint approximations. It also presents an example problem demonstrating how to use these methods to compute the area under a curve, and provides practice problems for the reader to try applying the techniques.

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

12. Try This One
• Approximate the area under the curve of the
function
• Use N = 4 subintervals and left endpoints
• Use N = 4 and midpoints