Unformatted text preview: (a) rotated around the xaxis (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 xx 2 and g ( x ) = x 22 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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 Spring '07
 Hamilton
 Integrals, Force, natural length

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