# Math172-Spring-2010-Exam1 - Math 172-01 Exam 1 Spring 2010...

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Math 172-01 Exam 1 Spring 2010 Name: ID: Date: Directions: Show all work. No work equals no credit. You may use a basic scientific calculator, but no graphing calculators. Use proper notation. 1. (20 pts) Using an appropriate method (please state the method used and sketch the volume of revolution), setup (but do not evaluate) integrals that represent the volume generated by revolving the region bounded by y = x - x 2 , y = 1, the y -axis, and x = 1, revolved about 0 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 x (a) the x -axis (b) the y -axis (c) the line x = 1 (d) the line y = 2
2. (9 pts) Find the length of the curve y = 1 3 ( x 2 + 2) 3 / 2 on the interval 0 x 3. 3. (9 pts) Find the surface area generated by the curve y = x + 1, for 0 x 5 when revolved about the x -axis: 4. (10 pts) If the switch is thrown open after the current in an RL circuit has built up to its steady- state value I = V/R , the delaying current i obeys the differential equation L di dt + Ri = 0. Note that R = 10 resistance and L = 20 inductance are constant.