Jay James Mike Norton Stephen Nesemann Kaitlyn Richardson

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Presentation transcript:

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

4.2 Area Equations:

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

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

For Extra Information… Watch these videos: http://www1.teachertube.com/viewVideo.php?video_id=213377&title=The_Trapezoid_Rule http://www1.teachertube.com/viewVideo.php?video_id=71388&title=Riemann_Sums