Integration WORD PROBLEM

Question

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

T(min) 1 6 11 16 21 26 31

V'(t) (L/min) 7 7 6 10 6 5 3

Approximate the total volume of water that passed through the dam from t = 1 to t = 31 using the simpsons rule with n = 6. ? in liters

Answer 1

The integral is equal to (h / 3) * [f(t₀) + 4f(t₁) + 2f(t₂) + 4f(t₃) + 2f(t₄) + 4f(t₅) + f(t₆)]

where:

1. h = 5 (the interval between the t values)
2. h is also obtained by taking (b - a) / n where b = 31, a = 1, and n = 6
3. f(t) is V'(t), the rate of water flow

After plugging in h and the V'(t) values from the table, you should get approximately 203.33 liters.

Hope this was helpful.