The following table shows the rate of water flow (in L/min) through a dam

Question

The following table shows the rate of water flow (in L/min) through a dam.

t (min) 1. 4. 7. 10. 13. 16. 19

V'(t) (L/min) 1. 2. 4. 3. 10. 1. 3

Approximate the total volume of water that passed through the dam from t=1 to t=19 using Simpson's rule, with n=6.

The answer is in liters

Answer 1

Simpson's rule gives S₆ = (b-a) / (3•6) • [f(x₀) + 4 f(x₁) + 2 f(x₂) + 4 f(x₃) + 2 f(x₄) + 4 f(x₅) + f(x₆)] = (19-1)/18 • [1 + 8 + 8 + 12 + 20 + 4 + 3] = 56 Liters.