Calculus - quiz tommorow please help

Question

Question 1. Use Simpson's Rule and all the data in the following table to estimate the value of the integral ` \int_(14)^(20)y dx`.

x14	15	16	17	18	19	20
y9	-2	-7	0	9	-4	-1

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Question 2.

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)7	3	8	6	9	5	2

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

__________________  liters

Answer 1

By Simpson's rule with n = 6,

S₆ = (Δx/3) * [ f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + 2f(x₄) + 4f(x₆) + f(x₇) ]

We can use this formula for both problems.

For Question 1, Δx = 1, since each subinterval has a width of x = 1.

S₆ = (1/3) * [ 9 + 4*(-2) + 2*(-7) + 4*0 + 2*9 + 4*(-4) + -1 ]

S₆ = -4 L

For Question 2, Δx = 1 also.

S₆ = (1/3) * [ 7 + 4*3 + 2*8 + 4*6 + 2*9 + 4*5 + 2 ]

S₆ = 33