Calc05_4 - Ch 5.4 Fundamental Theorem of Calculus dy dx = 3...

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Ch 5.4 Fundamental Theorem of Calculus

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dy dx = 3ξ 2 χοσξ 3 dy dx = 3 σινξ ( 29 2 χοσξ dy dx = 0 dy dx = 0 dy dx = 3 ξ λν3 dy dx = χοσξ + ξσινξ χοσ 2 dy dx = χοστ ( 29 / 2 dy dx = 1/ 2ξ ( 29
The Fundamental Theorem of Calculus, Part 1 If f is continuous on , then the function [ ] , a b ( 29 ( 29 x a F x f t dt = ò has a derivative at every point in , and [ ] , a b ( 29 ( 29 x a dF d f t dt f x dx dx = = ò

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( 29 ( 29 x a d f t dt f x dx = ò First Fundamental Theorem: 1. Derivative of an integral.
( 29 ( 29 a x d f t dt x f x d = ò 2. Derivative matches upper limit of integration. First Fundamental Theorem: 1. Derivative of an integral.

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( 29 ( 29 a x d f t dt f x dx = ò 1. Derivative of an integral. 2. Derivative matches upper limit of integration. 3. Lower limit of integration is a constant. First Fundamental Theorem:
( 29 x a d f t dt f x dx = ò 1. Derivative of an integral. 2.

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Calc05_4 - Ch 5.4 Fundamental Theorem of Calculus dy dx = 3...

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