Question 1 (Essay Worth 10 points) (06.01) Find the area of the region bounded by the curves y = sin '[ ], y = 0, and x = 6 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 1 6 Question 2 (Essay Worth 10 points) (06.02) Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = 3. Question 3 (Essay Worth 10 points) (06.02) The base of a solid in the xy-plane is the rst-quadrant region bounded y = x and y = x2. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid? Question 4 (Essay Worth 10 points) (06.03) Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x3 9x on the interval [1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. Question 5 (Essay Worth 10 points) (06.03) An object has a constant acceleration of 30 ft/secz, an initial velocity of 10 ft/sec, and an initial position of 4 ft. Find the position function, s(t), describing the motion of the object