Which of the following is the correct approximate for using the midpoint rule with n = 4? A. 0.425
B. 1.500
C. 0.625
D. 0.288

See the graph attached.

The midpoint rule states that you can calculate the area under a curve by using the formula:

In your case:

a = 0

b = 1

n = 4

x₀ = 0

x₁ = 1/4

x₂ = 1/2

x₃ = 3/4

x₄ = 1

Therefore, you'll have:

Now, to evaluate your f(x), you need to look at the graph and notice that:

f(x) = x - x³

Therefore:

M₄ = 1/4 · (2 - 478/512)

    = 0.2666

Hence, the area of the region bounded by y = x³ and y = x is approximately 0.267 square units.

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32