To approximate the area under the curve y=x^3 from x=3 to x=6, we can use the midpoint rule with four subintervals.First, we need to find the width of each subinterval:delta x = (6 - 3) / 4 = 0.75Next, we can find the midpoint of each subinterval:x1 = 3 + 0.5 * delta x = 3.375
x2 = x1 + delta x = 4.125
x3 = x2 + delta x = 4.875
x4 = x3 + delta x = 5.625Now, we can evaluate the function at each midpoint:y1 = x1^3 = 40.39
y2 = x2^3 = 71.25
y3 = x3^3 = 106.29
y4 = x4^3 = 146.48Finally, we can use the midpoint rule formula to approximate the area:A ≈ delta x * (y1 + y2 + y3 + y4)
= 0.75 * (40.39 + 71.25 + 106.29 + 146.48)
= 267.98Therefore, the approximate area under the curve y=x^3 from x=3 to x=6 is 267.98 square units.