In the figure, the equation of the solid parabola is y = x-2 and the equation of the dashed line is y = x. Determine the area of the shaded region. The area of the shaded region is (Type an exact answer.) Find the volume of the solid generated by revolving the region bounded by y = 2x, y = 0, and x = 4 about the x-axis. Set up the integral that gives the volume of the solid. 0 dx (Type exact answers.) Ay 10- 8- 6- 4- 2- 0- 0 1 2 3 4 5 Find the volume of the solid generated by revolving the region R bounded by y = ex, y = 0, x = 0 and x = In 3 about the x-axis. Set up the integral that gives the volume of the solid. 0 dx (Type exact answers.) y=ex R In 3 Suppose a force of 60 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.2 m from its equilibrium position? c. How much work is required to stretch the spring 0.4 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from its equilibrium? a. k= (Type an integer or a decimal.) Find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial position. a(t)=7e, v(0)=-7, and s(0) = 9 v(t) =