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praexam1sp10141 - (a rotated around the x-axis(b rotated...

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Math 141 (Section 04) Practice EXAM 1 1. Consider the regions between y = x and y = x 2 - 4 x + 4 rotated around the x and y axes. Set up the integrals that give the volumes of both of these solids of revolution. DO NOT EVALUATE THESE INTEGRALS. 2. A spring with force constant 24 N/m is compressed from a length . 4 m greater than its natural length to a length . 6 m less than its natural length. Set up and evaluate the integral for the work done in compressing the spring. 3. Consider the region bounded by y = x 2 and y = 2 - x 2 . Find the volume when this region is (a) rotated around the x-axis
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Unformatted text preview: (a) rotated around the x-axis (b) rotated around the line x = 1. 4. a) Sketch the graph of the parametrized curve C given by x = 2 + 3 cos2 t, y =-3 + 3 sin 2 t for ≤ t ≤ π 4 . b) Find a curve y = f ( x ) through the point ( π/ 2 , 2) whose length integral is L = i π r 1 + (sin 2 x ) e 2 cos x dx. 5. Let f ( x ) = 1 + 2 x-x 2 and g ( x ) = x 2-2 x + 1, and let R be the region between the graphs of f and g on [0 , 2]. Find the center of gravity of R . 1...
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