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Sunday, October 26, 2008

Definite Integrals

Hello Benofschool here. Wow it's been a while since I last scribed so here I go.

We started off the class talking about Riemann and his sums. The Riemann Sums was the term given to the sum of the different areas of the graph between each interval that we created during the last few classes with M(r)s. Karras and Dr. Eviatar. More info about Riemann and his sums can be found in the link on the first slide.

Now onto the Integrals. We were introduced to a new notation called the Definite Integral Notation. It is supposed to be a funky looking Sigma notation with a few twists. In the notation it shows the main interval [a,b] in which we are finding the sum, the function being used, and the size of the intervals between the closed larger interval [a,b]. So the definition of this notation involves limits where the number of intervals between [a,b] is to an infinite amount. Since it is human impossible to do this (Nothing is impossible if you BELIEVE) we try to get as close as possible.

Okay to work with this notation we locate the section of the function in which we are investigating. The definition of the notation is to get the sum of f(x) multiplied by the change in x up to the nth interval. If you remember from previous classes, the more intervals that we include in our calculations lead to a more accurate estimation of the integral of a function.

We looked at a couple of examples in the next few slides and continued on to a bit of something new. Monotonous Functions are functions that either increase or decrease, but never both. These functions give us the ability to determine the margin of error in our estimations. This is because in Non-Monotonous Functions the margin of error will be useless because of the change in the rates of change. Since Monotonous Functions either increase or decrease they will have a error that can be determined. This error shows how many intervals are required to find the Integral. Depending on the function some might need more than others.

Homework is Chapter 3.3 and do questions 1, 2, 4, 5, 7, 11, 17. But do enough that you understand it. No point in doing too much or too little.

The next scribe will be .:. J + ME .:.

Good night and do not let the Cimex lectularii masticate your epidermis, imbibing your blood.

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