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4.4 The Fundamental Theorem of Calculus

4.4 The Fundamental Theorem of Calculus. Essential Question : How are the integral & the derivative related?. The Fundamental Thm, Part 1:. If f is continuous on [ a , b ], then. where F  = f. Ex 1 : Find the area under the parabola y = x 2 from 0 to 1. Ex 2 :

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4.4 The Fundamental Theorem of Calculus

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  1. 4.4 The Fundamental Theorem of Calculus

  2. Essential Question: How are the integral & the derivative related?

  3. The Fundamental Thm, Part 1: If f is continuous on [a, b], then where F = f.

  4. Ex 1: Find the area under the parabola y = x2 from 0 to 1.

  5. Ex 2: Evaluate the integral.

  6. Ex 3: Evaluate the integral.

  7. The Fundamental Thm, Part 2: IF

  8. The Fundamental Thm, Part 2: AND f is continuous on [a, b], THEN g is continuous on [a, b] AND differentiable on (a, b), AND …

  9. The Fundamental Thm, Part 2: g (x) = f (x) WOW!

  10. Ex 4: Sketch the graph of g.

  11. Ex 5: Find the derivative of g.

  12. Ex 6: Find

  13. HW: 4.4 pg. 291 # 5 – 25 EOO, #27 – 37 odds, #51, 55 – 59 all, #67 – 93 odds, 74

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