Use the mid-point rule with n = 2 to approximate the area of the region bounded by y equals the cube root of the quantity 16 minus x cubed y = x, and x = 0.

Answer 1

f(x) = (16-x^3)^(1/3) - x

the partitions are (0,1) U (1,2)

the midpoints are at X1 = 0.5 and x2=1.5

SUM of deltaX * f(Xi) =

1 * f(0.5) + 1*f(1.5) =

f(0.5) + f(1.5) =

2.0132628476567395905687034358119 + 0.828504754

= 2.841767602