Using Simpsons Rule, answer the following question:

1)

The cross-sectional area of a fin is described by the area enclosed by the curves: y = x √(4-x), and the x-axis

Each unit of the function is equivalent to 10 cm of actual length. If the fin is made from rigid Kevlar Fibre 1 cm thick, and Kevlar fibre costs $3.00 per square unit. can she keep her material costs for each fin below $25.00

My attempt:

Simpsons Rule: A ≈ ((b-a) / 3n) [ yo + 4*[sum of odd y's] + 2*[sum of even y's] + yf]

y = x √(4-x)

x-intercepts are 0 and 4, therefore b = 4, and a = 0

Using n = 4, my intervals are each (4-0/4) units long or 1 unit

y(0) = 0

y(1) = 1.73

y(2) = 2.82

y(3) = 3

y(4) = 0

Area ≈ 1/3 [ 0 + 4(1.73 + 3) + 2(2.82) + 0]

Area ≈ 8.18 square units, and since each unit = 10cm, the cost is equal to: $3.00 * (10*8.18) = $245.4

This is above $25.00, therefore she will not meet the budget.

What have I done wrong?