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Unformatted text preview: , ( [ dy dx y x f , then ∫ ∫ = 1 1 1 ] ) , ( [ dx dy y x f ” Justify shortly your answer. (b) [6 marks] Evaluate dydx y x ∫ ∫ + 4 2 3 1 6 6. (a) [3 marks] Give the precise definition of the notion that the set 2 R Z ⊂ has “zero content” and prove that if 2 1 R Z ⊂ and 2 2 R Z ⊂ have zero content, then 2 1 Z Z ∪ has also zero content. (b) [5 marks] Let = = = otherwise n some for y x if y x f n n 1 ... 3 , 2 , 1 , ) ( ) , ( ) , ( 2 2 1 , 2 1 . Show that f is integrable on the rectangle ] 2 , [ ] 1 , [ × = E and determine the value of I = ∫ ∫ E dx y x f ) , ( . You may use any known theorems/properties without the proof, but you have to formulate them. ← Use the reverse side of the previous page if you need more space 7...
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This note was uploaded on 10/21/2010 for the course MATHEMATIC MAT237Y1 taught by Professor Romauldstanczak during the Fall '09 term at University of Toronto.
 Fall '09
 RomauldStanczak
 Calculus, Derivative

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