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 ∫ a b F 0 ( x ) g ( x ) d x where F 0 ( x ) (the weight) is a continuous and positive function and g ( x ) is twice continuously differentiable function in the interval [ a , b ] . Numerical examples are given to show the effectiveness of the method.