∫³ʰ₋ₕ f(x) dx ≈ w0 f(0) + w1 f(h) + w2f(2h)
Show that the formula with weights w1 = W3 = 8/3h and W2 -4/3 h is exact for all cubic functions. Then, assuming an error term of the form E = Kh⁵f⁽⁴⁾ (ε), with f⁽⁴⁾ the 4th derivative of f and ε ∈ (-h, 3h), use an appropriate function f to show that the constant K = 14/45