Truman College - Mathematics Department Math 208-AB: Calculus & Analytic Geometry II Classroom Activity #05 Instructor: Dr. Abdallah Shuaibi Fall 2014 ————————————————————————————————————— 1. Find the center of mass of the region bounded by the line y = x, and the parabola y = x2 . [δ(x) = 2x2 ] 2. When a particle is located a distance x feet from the origin, a force of x2 + 2x pounds acts on it. How much work is done in moving it from x = 1 to x = 3. 3. A tank has the shape of an inverted circular cone with height 10m and base radius 4m. It is filled with water to a height of 8m. Find the work required to empty the tank by pumping all of water to the top of the tank. (The density of water is 1000kg/m3 ) 4. Find the center of mass of each region. [δ(x) = 1] (a) the triangle with vertices (0,0), (4,0), and (4,6). (b) the region bounded by y = 4 − x2 , and y = 0. (c) the region bounded by y = x, y = −x, and x = 4.