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The Chalkboard Of Integrals

The Chalkboard Of Integrals. Michael Wagner Megan Harrison. What Is An Integral?. The limit of an increasingly large number of increasingly smaller quantities, related to the function that is being integrated. Area Under A Curve Sum of an infinite number of rectangles .

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The Chalkboard Of Integrals

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  1. The Chalkboard Of Integrals Michael Wagner Megan Harrison

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

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

  4. Who invented Integrals • Bonaventura Cavalieri (1598-1647) • 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 (1646 - 1716) • An indefinite fundamental theorem Sir Isaac Newton (1642 - 1727) • A defined fundamental theorem

  5. Why do we need integrals 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? 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?

  6. Properties of Calculus

  7. Properties of Calculus

  8. Properties of Calculus . . Remember that if you just use these simple properties any integral is easy 

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

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

  11. Multiple Choice Examples

  12. Multiple Choice Examples

  13. Multiple Choice Examples

  14. Ha Ha Laugh

  15. Helpful websites http://www.math.wpi.edu/IQP/BVCalcHist/calc2.html http://www.teacherschoice.com.au/Maths_Library/Calculus/calculate_definite_integrals.htm http://science.jrank.org/pages/3618/Integral.html http://cs.smu.ca/apics/calculus/welcome.php

  16. The End  Now you know a little bit of Calculus 

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