14209an6.10-12

# 14209an6.10-12 - of a continuous function f on the interval...

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c ± Kendra Kilmer April 2, 2009 Section 6.5 - The Fundamental Theorem of Calculus Fundamental Theorem of Calculus If f is a continuous function on [ a , b ] , and F is any antiderivative of f , then Example 1: Evaluate the following: a) Z 3 - 2 ( - x 2 + 4 ) dx b) Z 4 0 ( 4 t + t ) dt c) Z 5 1 ( e x + x ) dx 10

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c ± Kendra Kilmer April 2, 2009 d) Z 2 0 ( 2 x + 3 ) 6 dx Finding Deﬁnite Integrals on the Calculator: You can estimate the value of the deﬁnite integral Z b a f ( x ) dx by using the following command from your homescreen Example 2: Use the calculator to check our answers from Example 1. 11
c ± Kendra Kilmer April 2, 2009 Deﬁnition: The average value
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Unformatted text preview: of a continuous function, f , on the interval [ a , b ] is given by Example 3: Find the average value of the given functions on the given intervals a) f ( x ) = 5 on [ , 2 ] b) f ( x ) =-2 x 3 + x on [-2 , 1 ] a) f ( x ) = √ x + 2 on [ 2 , 7 ] Example 4: Given the supply function p = 10 ( e . 02 x-1 ) , ﬁnd the average price (in \$) over the interval [ 20 , 30 ] Section 6.5 Homework Problems: 5,11,17,23,29,35,41-47(odd),53,57,61,83 and supplemental prob-lems 12...
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14209an6.10-12 - of a continuous function f on the interval...

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