4 2 Area 4 3 Riemann Sums and

4. 2 Area 4. 3 Riemann Sums and Definite Integrals 4. 6 Numerical Integration Jay James Mike Norton Stephen Nesemann Kaitlyn Richardson

Equations: 4. 2 Area

Examples: evaluate ANSWER: 375

4. 2 Area • Let f be continuous and non-negative on the interval [a, b]. The area of the region bounded by the graph of f, the x-axis, x=a, and x=b is: Where and

Another Example Find the area under the curve for the equation bounded by the x axis on the interval [2, 5]. ANSWER: 39/2 units squared

What is a Riemann Sum? • In mathematics, a Riemann sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral.

Reimann Sums and Definite Integrals • If f is closed on the interval from [a, b] and the limit exists… • Then f in integrable on [a, b] and the limit is denoted by

Things You Should Know! • When plugging numbers into your equation you will want to know that. . • And…

Yet Another Example • Find using Riemann Sums: Answer= -3

4. 6 Numerical Integration Trapezoidal Rule • Rule:

Example: • Find using Trapezoidal method: n=4 Answer: about 3. 241

For Extra Information… • Watch these videos: • http: //www 1. teachertube. com/view. Video. ph p? video_id=213377&title=The_Trapezoid_Rul e • http: //www 1. teachertube. com/view. Video. ph p? video_id=71388&title=Riemann_Sums