University of MD University College Calculus II - Math 141 Quiz # 2 (100 pts) Dr. Ahmed Mohamed Summer 2017 07/07/2017 (Show all your work. This quiz Ch 5 covers material from week 2) 1. (20 pts) Find the volume of the solid formed by revolving the region bounded by f ( x) 2 x 2 and g ( x) 1 about the line y 1 . (Use the disk method) Find the exact arc length of the parametric curve without eliminating the parameter. 2. (20 pts) x cos 2t , y sin 2t 3. (20 pts) Find the center of mass of a system of point masses located at m1 6 , m2 3 , m3 2 and m4 9 , 4. (20 pts) of 3 , 2 , 0 , 0 , 5 , 3 and 4 , 2 Find the volume of the solid formed by revolving the region bounded by the graph about the . (Use the washer method) x axis y x and y x 2 5. (20 pts) 0 t 2 A spring exerts a force of 5 N when stretched 1 m beyond its natural length. a) Find the spring constant k . b) How much is required to stretch the spring 1.8 m beyond its natural length? . 6. Find the values of x between 1 and 5 so (a) tan(x) = 8, and (b) tan(x) = -3