assignment5

assignment5 - MATH1211/10-11(2)/A5/NKT THE UNIVERSITY OF...

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MATH1211/10-11(2)/A5/NKT THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 2nd Semester: Assignment 5 Due date: 2011 April 4 (Monday), 5:00pm. (The Exercise/problem numbers in the following refer to those in the textbook.) 1. ( § 5.2 no.28) (a) Show that if R = [ a,b ] × [ c,d ], f is continuous on [ a,b ], and g is continuous on [ c,d ], then ZZ R f ( x ) g ( y ) dA = ±Z b a f ( x ) dx ²±Z d c g ( y ) dy ² . (b) What can you say about RR D f ( x ) g ( y ) dA if D is not a rectangle? More specifically, what if D is an elementary region of type 1? 2. ( § 5.3 no.16) Evaluate Z π 0 Z π y sin x x dxdy . 3. ( § 5.4 no.18) Integrate f ( x,y,z ) = z over the region bounded by z = 0 , x 2 + 4 y 2 = 4 and z = x + 2. 4. ( § 5.5 no.26) Find ZZZ W dV p x 2 + y 2 + z 2 where W is the region bounded by the two spheres x 2 + y 2 + z 2 = a 2 and x 2 + y 2 + z 2 = b 2 , with 0 < a < b . 5. (
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This note was uploaded on 05/04/2011 for the course MATH 1211 taught by Professor Wang during the Spring '11 term at HKU.

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