Calculas Note - = ) ( x A intervals Example 1: 2 x y = Find...

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T HE A REA P ROBLEM tangent lines differential calculus rates of change Calculus (Fundamental Theorem of Calculus) - Method of exhaustion (Archimedes 287 BC-212BC) Area (rectangle method – sum of areas) - Antiderivative method - ) ( ) ( x f x A = (derivative of area function) integral calculus - Antidifferentiation (Integration) – finding the function when the derivative is known volume definite integral antidifferentiation Integration – The Area Problem ) ( x f ) ( x A A = Area Problem a b Rectangular Method Divide the interval into n subintervals As n gets bigger, the approximation gets better
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Unformatted text preview: = ) ( x A intervals Example 1: 2 x y = Find the area between 0 and 1. If n = 4, then 1 , 4 3 , 2 1 , 4 1 = x so Now do ,...... 1000 , 100 , 10 = n *GDC 2 nd STAT MATH, Sum, 2 nd STAT OPS, seq( sum(seq( )) 100 1 , 1 , , , 2 x x =33.835 = length then ( 29 33835 . 100 1 835 . 33 = Using Antiderivatives to find Area Example 1: find area on the interval [ ] x , 1-a) 2 ) ( = x f 2 ) ( = x f b) 1 ) ( + = x x f c) 3 2 ) ( + = x x f Assign: p.354 #1-17 odds...
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This note was uploaded on 07/12/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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Calculas Note - = ) ( x A intervals Example 1: 2 x y = Find...

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