# Use the mid-point rule with n = 4 to approximate the area of

Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x^3 and y = x?Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x^2 and y = x about the line x = 5? Find the area bounded by the curves y^2 = 2x + 6 and x = y + 1. Your work must include an integral in one variable?