MAC 2312 Midterm: MAC2312 C06 Test 1
Document Summary
Instructions: write your complete solutions on this paper. No graphing calculator is allowed to be used. To receive credit, you must show all work. You are not required to simplify your answers. Assume all physical units (length, force, etc. ) are in the mks system, hence are compatible. (1) (20 pts. ) Find y, the y-coordinate of the centroid of r. Let r denote the region between the curves y = 2x2 and y = 1+x where 0 x 1. Sketch the graph of r, showing a typical approximating rectangle. (a) find the area of r. (b) find my, the moment of r about the y-axis. A tank has the shape of an inverted right circular cone of height: the circular top is horizontal and has diameter 8. Assume the tank contains a liquid to a depth of 6. Take the density of the liquid to be .
