Calc05_4.ppt - 5.4 Fundamental Theorem of Calculus Morro...

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5.4 Fundamental Theorem of Calculus Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 1998 Morro Rock, California
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If you were being sent to a desert island and could take only one equation with you, x a d f t dt f x dx might well be your choice. Here is my favorite calculus textbook quote of all time, from CALCULUS by Ross L. Finney and George B. Thomas, Jr., ©1990.
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The Fundamental Theorem of Calculus, Part 1 If f is continuous on , then the function , a b x a F x f t dt has a derivative at every point in , and , a b x a dF d f t dt f x dx dx
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x a d f t dt f x dx First Fundamental Theorem: 1. Derivative of an integral.
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a x d f t dt x f x d 2. Derivative matches upper limit of integration. First Fundamental Theorem: 1. Derivative of an integral.
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a x d f t dt f x dx 1. Derivative of an integral.
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