5.4 - The Fundamental Theorem of Calculus - Hass

# 5.4 - The Fundamental Theorem of Calculus - Hass - Find the...

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11/11/2009 1 The Fundamental Theorem of Calculus Section 5.4 The Fundamental Theorem of Calculus If a function f is continuous on the closed interval [a,b] and F is an antiderivative of f on the interval [a,b], then ). ( ) ( ) ( a F b F dx x f b a = Examples • #14 • #22 • #28 • #32 Average Value of a Function If f is integrable on the closed interval [a,b], then the average value of f on the interval is . ) ( 1 b a dx x f a b Example

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Unformatted text preview: Find the average value of x x f 2 1 ) ( = over the interval [1,4]. Now go back and work #55, 57, & 59 from section 5.3. The 2 nd Fundamental Theorem of Calculus If f is continuous on an open interval I containing a , then, for every x in the interval, ) ( ) ( x f dt t f dx d x a = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ∫ 11/11/2009 2 Area Between Two Curves...
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5.4 - The Fundamental Theorem of Calculus - Hass - Find the...

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