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Unformatted text preview: c = 2(1 3 c √ c + c √ c ) = 4 3 c √ c. Set 4 3 c √ c = 32 3 . i.e. c √ c = 8 . Thus c = 4 . 4 4. Find the volume of the solid obtained by rotating about the xaxis the region in the ﬁrst quadrant enclosed by x = 1 , x = 2 , y = 1, and y = 1 /x . Volume = Z 2 1 π (1 2± 1 x ² 2 dx = π Z 2 1 (11 x 2 dx = π ( x + 1 x ) i 2 1 = π (2 + 1 2(1 + 1)) = π 2 5 5. Find the average value of the function f ( x ) = √ x on the interval [0 , 1]. Average = 1 1Z 1 √ x dx = 2 3 x 3 2 i 1 = 2 3 6 6. Sketch the curve with the polar equation r = sin( θ/ 2). 7...
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 Fall '08
 Justin
 Calculus, Cartesian Coordinate System, Polar coordinate system, dx, Calculus of Science and Engineering

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