Analysis of an algorithm is to determine the amount of resources such as time and storage necessary to execute it. The efficiency or complexity of an algorithm is based on the function relating the input length to the number of operations to execute the algorithm. In this paper, the computational complexities and execution time for sequential and parallel algorithms used Numerical Quadrature Formulas on Multi Core system Using Open MP are analyzed.To find the integral value of various function using Trapezoidal Rule, Simpson 1/3 Rule, Simpson’s 3/8 Rule, Boole’s Rule.We have to calculate estimated execution time taken by the programs of sequential andparallel algorithms and also computed the speedup. Accuracy of thequadrature formulas has been found in the order- Simpson’s three-eighth rule > Simpson’sone-third rule > Boole’s rule > Trapezoidal rule.