# A4 - -1(1 0 and(0 1 is rotated about the line x = 2 3 Find the length of the given curves in parts(a)–(c(a y = ln cos x from x = π 6 to x = π

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Math 128: Assignment 4 due Th, Oct. 13 by 4:30 pm Koray Karabina ([email protected]) 1. Find the areas of the regions described in parts (a)–(e). (a) The region bounded by y = x 3 , x = y 2 . (b) The region bounded by y = 1 /x , 2 x + 2 y = 5. (c) The region bounded by y = sec 2 x , y = sin x between the values of x = 0 and x = π/ 4. (d) The region bounded by y = x 2 - 2 x , y = 2 x - 3. (e) The region below y = 0 and above y = ln x , to the right of x = 0. 2. Find the volumes of the solids described in parts (a)–(e). (a) The region bounded by y = x and x = 4 y - y 2 is rotated about the x -axis. (b) The region bounded by y = x and x = 4 y - y 2 is rotated about the y -axis. (c) The region bounded by y = 1 / (1 + x 2 ), y = 2, x = 0, and x = 1 is rotated about the x -axis. (d) The region bounded by y = 1 / (1 + x 2 ), y = 2, x = 0, and x = 1 is rotated about the y -axis. (e) The triangular region with vertices (0
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Unformatted text preview: ,-1), (1 , 0) and (0 , 1) is rotated about the line x = 2. 3. Find the length of the given curves in parts (a)–(c). (a) y = ln cos x from x = π/ 6 to x = π/ 4. (b) x = y 3 / 2 from y = 0 to y = 4. (c) y 2 = 4 x 3 from y =-2 to y = 16. 4. Find the circumference of the closed curve x 2 / 3 + y 2 / 3 = a 2 / 3 . 5. In parts (a)–(e), ﬁnd the areas of the surfaces obtained by rotating the curve about the indicated axis. (a) y = x 3 / 2 , (0 ≤ x ≤ 1), about the y-axis. (b) y = e x , (0 ≤ x ≤ 1), about the x-axis. (c) y = sin x , (0 ≤ x ≤ π ), about the x-axis. (d) x = y 3 , (1 ≤ y ≤ 2), about the y-axis. (e) y 2 + x = 4, (0 ≤ x ≤ 4), about the x-axis....
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## This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.

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