Problems on Area Volume and Length From Old Exams

# Thomas' Calculus: Early Transcendentals

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Mat104 Fall 2002, Problems on Area, Volume and Length From Old Exams (1) (a) The region S bounded by y = sec x and the x -axis for - π/ 4 x π/ 4 is rotated around the x -axis. Find the volume of the resulting solid. (b) The region R bounded by the parabolas y 2 = x and y 2 = 2 x - 6 is rotated about the x -axis. Find the volume of the resulting solid. (2) Find the arc length of the of the curve given by x = e 2 t sin 2 t , y = e 2 t cos 2 t for 0 t 1. (3) The region enclosed between the curve y = e - x and the lines x = 1 and x = 2 is rotated around the x -axis. Find the volume of the resulting solid of revolution and the surface area of the boundary of this solid. (4) Let R be the region above the x -axis, to the right of the y -axis, and below the circle of radius 1 and center (1 , 1). Find the area of R . Find the volume of the solid S obtained by rotating the region R around the x -axis. Find the surface area of this solid S . (5) Let R be the region bounded by the lines y = 0, y = 1, x = 2 - y , and the curve x = y .

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• Fall '07
• Nelson
• Region, x-axis

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