1. Jay James Mike Norton Stephen Nesemann Kaitlyn Richardson
4.2 Area 4.3 Riemann Sums and Definite Integrals 4.6 Numerical Integration
Jay James
Mike Norton
Stephen Nesemann
Kaitlyn Richardson

2. 4.2 Area
Equations:

3. Examples:
evaluate
ANSWER: 375

4. 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

5. 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

6. 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.

7. 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

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

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

10. 4.6 Numerical Integration Trapezoidal Rule

11. Example:
Find using Trapezoidal method:
n=4
Answer: about 3.241

12. For Extra Information…
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