Question

Simpson's Rule arc length calculator - What is the formula for calculating the arc length using Simpson's Rule?

a) L = h/3 [f(x₀) + 4f(x₁) + 2f(x₂) + ... + 2f(xₙ-2) + 4f(xₙ-1) + f(xₙ)]
b) L = h/2 [f(x₀) + 4f(x₁) + 2f(x₂) + ... + 2f(xₙ-2) + 4f(xₙ-1) + f(xₙ)]
c) L = h [f(x₀) + 4f(x₁) + 2f(x₂) + ... + 2f(xₙ-2) + 4f(xₙ-1) + f(xₙ)]
d) L = h/4 [f(x₀) + 4f(x₁) + 2f(x₂) + ... + 2f(xₙ-2) + 4f(xₙ-1) + f(xₙ)]

Answer 1

The formula for calculating the arc length using Simpson's Rule is L = h/3 [f(x₀) + 4f(x₁) + 2f(x₂) + ... + 2f(xₙ-2) + 4f(xₙ-1) + f(xₙ)].

Step-by-step explanation:

The correct formula for calculating the arc length using Simpson's Rule is option a) L = h/3 [f(x₀) + 4f(x₁) + 2f(x₂) + ... + 2f(xₙ-2) + 4f(xₙ-1) + f(xₙ)]. Simpson's Rule is an approximation method used to estimate the arc length of a curve. It involves dividing the curve into multiple subintervals and using a weighted average of the function values at the endpoints and midpoint of each subinterval.