Consider the solid region S that lies under the surface z = 8x vy and above the rectangle R = [0, 2] x [1, 4]. (a) Find a formula for the area of a cross-section of S in the plane perpendicular to the x-axis at x for 0 s x s 2. (Use the value k for x.) x dy Use the formula to compute the areas of the cross-sections illustrated. k = 1 k = 2 (b) Find a formula for the area of a cross-section of S in the plane perpendicular to the y-axis at y for 1 s y s 4. (Use the value k for y.) ZA X dx Use the formula to compute the areas of the cross-sections illustrated. k = 1 k = 3 (c) Find the volume of S