LM 7.7

Question 1

What is the trapezoidal rule?

Answer 1

The integral from a to b of f(x) can be approximated by Δx/2[f(x₀) + 2f(x₁) + 2f(x₂)+…+2f(x_n-1) + f(x_n)} where Δx = (b-a)/n and x_i = a + iΔx

Question 2

What is Simpson’s Rule?

Answer 2

The integral from a to b of f(x) can be approximated by Δx/3[f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃)+…+2f(x_n-2) + 4f(x_n-1)+ f(x_n)} where n is even and Δx = (b-a)/n

Question 3

What is the midpoint rule?

Answer 3

The integral from a to b of f(x) can be approximated by Δx[f(x₁) + f(x2) + …f(x_n)} where Δx = (b-a)/n and x_i = 1/2(x_i-1 + x_i) = midpoint of 2 x values