lecture15

# lecture15 - MATH 100 Class 15 Double Integral over...

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2006 Fall MATH 100 Lecture 14 1 MATH 100 Class 15 Double Integral over non-rectangular region ∫∫ ∫∫ ∫∫ = = d c (y) h (y) h R b a (x) g (x) g R dxdy y x f dA y x f dxdy y x f dA y x f R f d y c (y) h x (y) h b x a (x) g y (x) g 2 1 2 1 ) , ( ) , ( region II For type ) , ( ) , ( region I For type : 1 Step ? over of integral the compute to How , : II type , : I type 2 1 2 1 non-rectangular regions:

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2006 Fall MATH 100 Lecture 14 2 MATH 100 Class 15 Double Integral over non-rectangular region Geometric explanation:
2006 Fall MATH 100 Lecture 14 3 MATH 100 Class 15 Double Integral over non-rectangular region 4 2 , 2 1 : Ex n. imaginatio little a just limit? up set to How ) , ( ) ( with ) ( ) , ( ( vol then 0, if 2 1 = = = = ∫∫ ∫∫ x x y x R xydA dy y x d x A dx x A dA y x f s) f R (x) g (x) g b a R

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2006 Fall MATH 100 Lecture 14 4 MATH 100 Class 15 Double Integral over non-rectangular region [] 6 11 2 4 32 1 2 4 6 1 4 4 1 3 1 2 1 4 2 2 1 4 4 3 3 4 2 4 3 4 2 2 4 2 2 / 2 4 22 / = = =
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## This note was uploaded on 09/17/2011 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

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lecture15 - MATH 100 Class 15 Double Integral over...

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