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Section 5.2 The Definite Integral

Section 5.2 The Definite Integral. AP Calculus November 19, 2009 Berkley High School, D1B1 todd1@toddfadoir.com. Summary. We learned that we can find the exact area on the interval [a,b] under a curve by taking the following limit…. The Riemann Sum.

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Section 5.2 The Definite Integral

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  1. Section 5.2The Definite Integral AP Calculus November 19, 2009 Berkley High School, D1B1 todd1@toddfadoir.com

  2. Summary • We learned that we can find the exact area on the interval [a,b] under a curve by taking the following limit… Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  3. The Riemann Sum • We call this limit “The Riemann Sum” named for Bernhard Riemann. Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  4. Function Slice of x Function Slice of x Sum (Integration) Sum (Sigma) The Definite Integral • Instead of the bulky Riemann notation, use the easier Leibniz notation Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  5. Your turn… Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  6. Your turn… Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  7. Your turn… Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  8. Your turn… Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  9. Your turn… Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  10. Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  11. “Negative Areas” Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  12. “Negative Area” Example Calculus, Section 5.2, Todd Fadoir, CASA, 2003

  13. Assignment • Section 5.2, 1-31, odd, X27 Calculus, Section 5.2, Todd Fadoir, CASA, 2003

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