1. (4 pts) Use the shell method to find the volume of the solid obtained by rotating the region bound by y = x and y = 2x about the y-axis. include a sketch of the 2D region, as well as a sketch of the 3D solid which includes the cross-section. 2. (3 pts) An object moves along the x-axis under the force given by f (x) = x (x2 - 1)" Find the work done in moving the object from x = 0 to x = 1 (HINT: Use the substitution method to integrate). 3. (3 pts) Find the average value of the function f (x) = (a + 1) on the interval [0, 3]. (HINT: Use the substitution method to integrate)