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The Fundamental Theorems of Calculus Lesson 5.4

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First Fundamental Theorem of Calculus Given f is continuous on interval [a, b] F is any function that satisfies F’(x) = f(x) Then

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First Fundamental Theorem of Calculus The definite integral can be computed by finding an antiderivative F on interval [a,b] evaluating at limits a and b and subtracting Try

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Area Under a Curve Consider Area =

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Area Under a Curve Find the area under the following function on the interval [1, 4]

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Second Fundamental Theorem of Calculus Often useful to think of the following form We can consider this to be a function in terms of x View QuickTime Movie View QuickTime Movie

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Second Fundamental Theorem of Calculus Suppose we are given G(x) What is G’(x)?

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Second Fundamental Theorem of Calculus Note that Then What about ? Since this is a constant …

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Second Fundamental Theorem of Calculus Try this

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Assignment Lesson 5.4 Page 327 Exercises 1 – 49 odd

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