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Unformatted text preview: : ] 1 , [ ] 1 , [ × ⎪ ⎩ ⎪ ⎨ ⎧ Ν ∈ = = = otherwise prime q with q n m some for q n y and q m x if y x f , , 1 ) , ( (a) Is f integrable on R ? Justify your answer. (b) Do both iterated integrals exist? Justify your answer. 3. Verify that the assumptions of the Fubini Theorem are satisfied and evaluate (a) , where ∫∫ D dxdy y x ) , 2 max( ] 1 , [ ] 2 , [ × = D . (b) ∫∫ , where D dxdy y E ) ( } 2 5 : ) , {( 2 2 ≤ ≤ ∈ = y x R y x D . Remark: denotes the integer part of the number u . ) ( u E 4. Evaluate dzdydx z z z x y ∫ ∫ ∫ − − 1 1 1 ) 2 ( ) sin( π (Be careful: Why does the triple integral even exist?) 5. Let . Find vol ( } 1 ..... : { 1 2 1 ≤ ≤ ≤ ≤ ≤ ≤ ∈ = Ω − x x x x R n n n x Ω ). Remark: Considering cases n = 2 and n = 3 first might be helpful....
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This note was uploaded on 12/21/2010 for the course MATH 237Y1 taught by Professor Stanczak during the Fall '09 term at University of Toronto.
 Fall '09
 STANCZAK
 Math

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