5.3 Notes - Fall 2002 - from a to b is defined as where f x...

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Survey of Calculus – Section 5.3 You know how to find the area of some regions such as rectangles, circles, triangles, etc. In this section we will learn how to find the area of irregular shaped regions. We will do this by approximating the area with rectangles. Example: Approximate the area under the curve from 1 to 2 by using 4 rectangles. Use rectangles with equal bases and with heights equal to the height of the curve at the left-hand edge of the rectangles. 2 3 ) ( 2 + = x x f Definite Integral Let be a continuous function on an interval [a,b]. The definite integral of
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Unformatted text preview: from a to b is defined as where f x f ( f [ ] x x f x x f x x f dx n n b a + + + = ) ( ) ( ) ( lim ) 2 1 L n b x = a , and are x-values beginning with and obtained by successive additions of . If is nonnegative on [a,b], then the definite integral gives the area under the curve from a to b. n x x x ,..., , 2 1 a = x x 1 f Fundamental Theorem of Integral Calculus For a continuous function on an interval [a,b], where is any antiderivative of . f ) ( ) ( ) ( a F b F dx x f b a = F f #18 #2 #26 #28 #46 #56 #74...
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This note was uploaded on 01/12/2012 for the course MATH 2043 taught by Professor Pamelasatterfield during the Fall '05 term at NorthWest Arkansas Community College.

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5.3 Notes - Fall 2002 - from a to b is defined as where f x...

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