ydx = (h/3) X {(y₀ + y_n) + [4 X (y₁ + y₃ +....+ y_{n - 1})] + [2 X (y₂ + y₄ +....+ y_n-2)]} OR

ydx = (h/3) X [(y₀ + y_n) + (4 X ODD) + (2 X EVEN)]

Q. 1. Compute the approximate value of the integral (June 2002)
I =(1 + x²) dx
using Simpson's rule by taking interval size h as one.

Solution.

Here, h = 1, y₀ = 1, y₁ = 2, y₂ = 5
y dx = (h/3) X [(y₀ + y₂) + (4 X y₁)]
or y dx = (1/3) X [(1 + 5) + (4 X 2)]
or y dx = 14/3

Q. 2. Compute the approximate value of the integral (Dec. 2001)
I =(1 + x + x²) dx
using Simpson's rule by taking interval size h as 1.

Solution.

Here, h = 1, y₀ = 1, y₁ = 3, y₂ = 7, y₃ = 13, y₄ = 21
y dx = (h/3) X {(y₀ + y₄) + [4 X (y₁ + y₃)] + (2 X y₂)}
or y dx = (1/3) X {(1 + 21) + [4 X (3 + 13)] + (2 X 7)}
or y dx =100/3