# hw8 - to the center of the disk is 2 a/ 3. b) Find the...

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Math 53 Homework 8 Due Wednesday 10/20/10 in section (The problems in parentheses are for extra practice and optional. Only turn in the underlined problems.) Tuesday 10/12 – Double integrals Read: sections 15.1, 15.2, 15.3. Work: 15.2: (5), 12 , 17 , 21 , (24), (25), (31). 15.3: (1), 3 , 6 , 8 , (13), 15 , (21), 23 , (33), 39 , (41), (45), 47 , (55), 58 . Thursday 10/14 – Double integrals in polar coordinates; applications Read: sections 15.4, 15.5. Work: 15.4: 6 , 7 , (11), (13), 17 , (22), 25 , (27), (29), 31 , (35), 36 . 15.5: (3), 8 , (11), 12 , 18 , (27), 28 . Problems 1 and 2 below. Problem 1. (The two parts are independent) a) Show that the average distance of a point in a disk of radius a
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Unformatted text preview: to the center of the disk is 2 a/ 3. b) Find the average distance of a point in a disk of radius a to a xed point on the circumference of the disk. (Hint: place the center of the disk at ( a, 0) and the given point on the circumference at the origin). Problem 2. a) Find the area of the region R bounded by the curve r = sin 2 in the rst quadrant. (Do this as a double integral in polar coordinates.) b) Find the coordinates ( x, y ) of its center of mass (take a uniform density = 1). (Hint: it is helpful to rewrite the value of the inner integral as the product of sin by an expression involving only cosines.)...
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## This note was uploaded on 03/14/2012 for the course MATH 113 taught by Professor Ogus during the Spring '08 term at University of California, Berkeley.

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