lecture14

lecture14 - MATH 100 Class 14 Double Integral Definite...

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2006 Fall MATH 100 Lecture 14 1 MATH 100 Class 14 Double Integral () () k n k k n b a x x f dx x f Δ = = +∞ 1 lim : integral Definite Geometric explanation: As n increases, The limit converges And error diminishes
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2006 Fall MATH 100 Lecture 14 2 () 0 and over continous is where , , surface a and plane - in the region a between bounded solid the of volume the Find : Problem = f R f y x f z xy R Approach: 1: cut R with lines parallel to the x and y axes, consider only those rectangles contained in R MATH 100 Class 14 Double Integral
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2006 Fall MATH 100 Lecture 14 3 () {} Sum Riemann ...... , form and , , r rectangula - sub each in point a arbitarily pick : 2 1 = Δ n k k k k k k A y x f y x () () k n k k k n A k n k k k n A y x f dA y x f R y x f A y x f V Δ = Δ = = = 1 1 , lim , Sum Riemann of limit the : over , of integral Double , lim by denote and cutting, the refine : 3 MATH 100 Class 14 Double Integral
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2006 Fall MATH 100 Lecture 14 4 ( ) ( ) ()() [] () ± = ± = R R R R R dA y x g dA y x f dA y x g y x f dA y x f
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lecture14 - MATH 100 Class 14 Double Integral Definite...

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