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4.4 The Fundamental Theorem of Calculus
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Essential Question: How are the integral & the derivative related?
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The Fundamental Thm, Part 1: where F = f. If f is continuous on [a, b], then
![The Fundamental Thm, Part 1: where F = f. If f is continuous on [a, b], then](http://images.slideplayer.com./27/8998792/slides/slide_3.jpg "The Fundamental Thm, Part 1: where F = f. If f is continuous on [a, b], then")
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Ex 1: Find the area under the parabola y = x 2 from 0 to 1.
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Ex 2: Evaluate the integral.
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Ex 3: Evaluate the integral.
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The Fundamental Thm, Part 2: IF
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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 …
![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 …](http://images.slideplayer.com./27/8998792/slides/slide_8.jpg "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 …")
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The Fundamental Thm, Part 2: g (x) = f (x) WOW!
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Ex 4: Sketch the graph of g.
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Ex 5: Find the derivative of g.
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Ex 6: Find
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HW: 4.4 pg. 291 # 5 – 25 EOO, #27 – 37 odds, #51, 55 – 59 all, #67 – 93 odds, 74
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