An extension of trapezoidal type product integration rules

In the present paper, we use a generalization of the Euler–Maclaurin summation formula for integrals of the form ∫abF0(x)g(x)dx where F0(x)F0(x) (the weight) is a continuous and positive function and g(x)g(x) is twice continuously differentiable function in the interval [a,b][a,b]. Numerical examples are given to show the effectiveness of the method.