(a) Find a function f (x) and a number k such that X f (t) 6+ t2 dt = 2vx k for x > 0. (b) Use the midpoint approximation method to find the area under the curve f(x) = 1 - x2 over the interval [-1, 1]. (c) Find the area of the region enclosed by x = y2 - 4y + 2 and x = y - 2. (d) Find the volume of the solid that results when the region enclosed by y = x3, x = 2, and y = 0 is revolved about the line x = 2 using: (i) the method of disks and (ii) cylindrical shells. (e) For the curve y = + - from x = 1 and x = 2 find the 12 X (i) arc length and (ii) surface area generated when the curve is revolved about the x-axis