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M21Ex4F98

# M21Ex4F98 - Math 21 1(16 points The curve C is given by the...

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Math 21 Exam 4 1. (16 points) The curve C is given by the parametric equations, x = e t . y = t , with t [0 , 1]. a) C is also given by the Cartesian equation y = F ( x ), for x [ c, d ]; where F ( x ) = c = d = b) Give, but do not evaluate, an integral that give the length of C . The limits of integration and the integrand must be explicit, the integrand containing only the variable of integration. Length = c) Give, but do not evaluate, an integral that gives the area of the surface obtained by revolving C around the y -axis. The limits of integration and the integrand must be explicit, the integrand containing only the variable of integration. Area = 2. (14 points) Let R be the region bounded by y = cos x , x = 0, x = π , and y = 0. Let ρ = 2. The coordinates, (¯ x, ¯ y ), for the centroid of R are given by ¯ x = M Y M ¯ y = M X M Give, but do not evaluate, the integrals for M , M X , and M Y . The limits of integration and the integrand must be explicit, the integrand containing only the variable of integration.

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