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Unformatted text preview: (c) (10 points) Evaluate I = ZZ R p x 22 xy + 5 y 2 dA using the transformation T . 2 Problem 3 (25 points) Find the work done by the force ﬁeld F ( x,y ) = 3 x 2 i + (4 x + y 2 ) j on a particle that moves along the following paths: (a) (10 points) C 1 is the line segment from (1 , 0) to (0 , 1). (b) (15 points) C 2 is part of the curve x 2 + y 2 = 1 for which x ≥ 0 and y ≥ 0 (the particle moves counterclockwise). 3 Problem 4 (15 points) Find the mass of a ball given by x 2 + y 2 + z 2 ≤ 9 if the density at any point, denoted by D ( x,y,z ), is proportional to its distance from the origin. Problem 5 (10 points) Using cylindrical coordinates set up, but do not evaluate the integral I = ZZZ E dV, where E is the region bounded above by x 2 + y 2 + z 2 = 4 and below by z = √ 2. 4 Bonus Problem 6 (10 points) Solve Problem 5 using spherical coordinates. 5...
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This note was uploaded on 04/24/2009 for the course CALC 2401 taught by Professor Stojanovic during the Spring '09 term at Georgia Tech.
 Spring '09
 Stojanovic
 Calculus

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