APPM 1360 Midterm: appm1360spring2018exam2_sol
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Spring 2018: (20 pts) the shaded disk shown below is rotated about the line x = 3, forming a torus (i. e. a doughnut shape). Set up (but do not evaluate) integral(s) representing the quantity in question. Leave your answers unsim- pli ed. (a) the volume of the torus using the shell method. (b) the surface area of the torus. Solution: a (a) v =z b (b) y = x. 2. (a) (12 pts) find the arc length of the curve y = 4x2 on the interval [1, 2]. (b) (8 pts) two objects are located on the x-axis. One object, of mass m, is located at x = 2. The other object has mass 3 and is located at x = 7. Solution: (a) (b) x = a y = 8 m + 3 m = m1 + m2 2 = 2m + 21.
