The Chalkboard Of Integrals Michael Wagner Megan Harrison.

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Presentation transcript:

The Chalkboard Of Integrals Michael Wagner Megan Harrison

Area Under A Curve Sum of an infinite number of rectangles The limit of an increasingly large number of increasingly smaller quantities, related to the function that is being integrated What Is An Integral?

Integrals have six parts 1. The Upper Limit B 2. The Lower Limit A 3. The Function f(x) 4. F(x) is the integral of f(x) 5. F(b) is the value of the integral at the upper limit, x=b 6. F(a) is the value of the integral at the lower limit, x=a What does it look like

Bonaventura Cavalieri ( ) Small rectangles under a line which would get so small they would be lines themselves. There are an infinite number of lines under a curve Gottfried Wilhelm Leibniz ( ) Who invented Integrals Sir Isaac Newton ( ) A defined fundamental theorem An indefinite fundamental theorem

Integrals allow us to determine where an object lies at rest after being fired How far did the rocket travel before is hit the ground? Why do we need integrals Integrals give us a tool to quantify the things around us How big are the Wasatch Mountains? How much dirt has been removed from Kennecott? Integrals allow us to determine the value of an item before we use it What is the maximum profit for a product? Integrals allow us to find the volume of an object What is the volume of a vase?

Properties of Calculus

.. Remember that if you just use these simple properties any integral is easy

Multiple Choice Examples Hint: Remember that the derivative of sin(x) is cos(x)

Mulitple Choice Examples Hint: (x^(n+1))/(n+1)

Multiple Choice Examples

Ha Ha Laugh

Helpful websites e_definite_integrals.htm

The End Now you know a little bit of Calculus