Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = -x^3 and y = -x

Answer 1

algebraically, the area is zero, since both functions are odd.
geometrically, we can use symmetry and just take twice the area in the 2nd quadrant.
That means we just need two rectangles, with boundaries at
x = 0, -1/2, -1
so the area is twice

(f(0)+f(-1/2))/2 * 1/2 + (f(-1/2)+f(-1))/2 * 1/2