Answer to Question #328998 in Calculus for Rohit

Question

Integrate (1/(x+1)) dx within the limits 0 to 4 in four parts using Simpson rule

Answer 1

Solution

For function f(x) with division interval [a,b] in four parts

h = (b-a)/4, x₀ = a, x₁ = a+h, x₂ = a+2h, x₃ = a+3h, x₄ = b

For given integral

h = 1, x₀ = 0, x₁ = 1, x₂ = 2, x₃ = 3, x₄ = 4

If f_i = f(x_i) = 1/(x_i+1) then integral value using Simpson rule is

I = (f₀+4f₁+2f₂+4f₃+f₄)/3

f₀ = 1, f₁ = 0.5, f₂ = 0.33333, f₃ = 0.25, f₄ = 0.2

Therefore I = 1.622

Exact value of given integral is ln(5) = 1.609

Solution I = 1.622