Worth 99 points! use the midpoint rule with n=4 to approximate the area of the region bounded by y=x^3 and y=x. must use the midpoint rule! , you.

The objective is to find total bounded area. Intersections occur at x=-1, x=0, and x=1. Since we need 4 subintervals, we split the line segment from -1 to 1 into four line segment.

That would be 

So subintervals would be
[-1, -0.5]
[-0.5, 0]
[0, 0.5]
[0.5, 1]

Since segment was split evenly, because of rotate symmetry, sub-area for [-1,0] and [0,1] would be same so we can just focus on interval [0,1] with n=2 and then multiple the result by 2.

Now we are talking about midpoint rules, the height of rectangle for [0,0.5], [0.5,1] would be  respectively. Width of rectangle would be .

Hence for , that would be


And  would be


So the approximate area is 0.28125.

Now double that to account for area from [-1,0] and our answer is 0.5625.

Is this clear?