### دراسة مقارنة لطرق التكامل العددي المحدود باستخدام برنامج MATLAB

#### Abstract

This paper view the primal idea about the numerical integration and numerical analysis. We take three limited integrals for example, the first is exponential function, the second is trigonometric function, and the last function is fraction. This functions were solved by the direct method using the integrations rules, so, the results which we obtained represents the exact values for these integrals, which represents the area under the curve of these functions and x-axis too. Then we solved these integrals using four numerical methods:1-Trapezoidal rule.2-Simpson’s rule.3-Midpoint rule.4-Romberg rule.We calculate the relative errors for these examples in order to make a comparison between the results using direct and numerical methods. We use here the MATLAB programs in numerical methods for each rule. When we write the results in a table, we found that the Romberg rule give us a good result approach to exact. Then we study the effect of layers increasing on the accuracy of the results, and we found that the value of the integrals is approached more to the exact value with the layers increasing.

MATLAB