MATH 2374 Midterm: MATH 2374 UMN Spring 07 Exam 2sol
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1 x2 (2xy + x)dy dx. x x2$ dx (2xy + x)dy dx = ! 1 (x3 + x2) (x5 + x3)dx x2 x5dx. There are two integrals that need to be evaluated in this problem, each one was worth 10 points. 2 &(cos t t sin t)2 + (sin t + t cos t)2 + 1dt = % 2 ||r! (t)||dt 5 points form; 1 point bounds. 2 + t2dt 4 points (ii) (15 points) suppose the density of the wire at the point (x, y, z) is (x, y, z) = z. Find the mass of the wire. (this should be an easy integral to calculate. ) 2 t 2 + t2dt (2 points for t, 3 points for 2 + t2) 2 2t 2 + t2dt = (1/2)(2/3)(2 + t2)3/2| 2 = 1/3(93/2 43/2) = 19/3 5 points: (20 points) reverse the order of integration for this integral:
