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Newton_Cotes Quadrature Formula

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Newton_Cotes Quadrature Formula:                  b     Let I = ∫ f(x) dx   ............(1)                 a Where f(x) takes the values y₀,y₁,y₂.....yₙ for x= x₀,x₁,x₂.........xₙ   Let us divide the interval (a,b) into n sub_intervals of width h so that  x₀=a , x₁= x₀+h , x₂=x₀+2h ......xₙ=x₀+nh=b               x₀+nh Then I= ∫ f(x) dx   Put x=x₀+rh ⇒dx =hdr               x₀                  n           = h ∫ f(x₀+rh) dr                 0                 n          = h ∫ [y₀+rΔy₀+r(r-1)/2! Δ²y₀                 0   ...