MAT 21B Midterm: MATH 21B Midterm Exam 2 Winter 2010 Solutions 2
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MAT 21B Full Course Notes
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In all three cases, we can use symmetry by computing the answer for the. Solution. part of the curve in the range 0 x 1 and multiplying it by 2. This gives (2 x)2 dx = 2 (2 x)3. 2 dx = 2 2, (c) l = 2z 1 (b) a = 2z 1. 0 t is revolved about the y-axis. The di erential arc-length is given by ds =pdx2 + dy2 =s(cid:18) dx dt(cid:19)2 so the surface area is dt(cid:19)2. +(cid:18) dy dt = t + t 1 dt =rt2 + 1 t dt, This integral can be computed by making the substitution u = t2 + 1, leading to. 9: a thin rod of length 2 meters is made of a material whose composition changes along the length of the rod. The density at distance x from the left end of the rod is f (x) = 100 + x2/200 grams per centimeter.
