Design of Simulation Definite Integral Application learning Using Trapezoid Method based on VB.Net

The definite integral is one of the subjects that is difficult for students to understand because the process of calculating definite integral of functions is quite complicated and long because it requires mastery of some integrating rules so an interactive learning simulation application is needed to make it easier for students to calculate definite integral of functions and the depiction of the area the curve. One method for calculating definite integrals is the trapezoid method. The trapezoid method works by dividing the boundary into 2 intervals namely x = x0 to x = x1. Simulation media application learning will be designed with the VB.Net programming language. This simulation media learning starts with reading and checking data input. The process is continued by displaying the depiction of the input curve and ending with calculating the area of the curve. Simulation media learning provides a facility to store the input data, the results of the calculation of the area and the image of the curve function in the image format of * .bmp. In this media, the media and material expert’s the results of the average are produced by 88.68% included into media category is very valid media and the results of pre-test and post-test trials showed an increase with an average value of 48.3 for pre-test and 87 for the post-test of the passing grade requirement of 70.Keywords: Definite Integral, Trapezoid Method,VB.Net, Media Validation.

ANALYSIS OF STABILITY OF ONE CLASS OF NUMERICAL METHODS OF SECOND ORDER

The paper deals with the analysis of the stability of a class of second order combined numerical methods based on the trapezoid method and the difference formula, what obtained by the author. The stability conditions for this class of methods are obtained by the example of conservative systems.

PERFORMANCE OF TRAPEZOIDAL METHOD AND GAUSS-LEGENDRE METHOD IN SETTLEMENT OF CERTAIN INTEGRAL ASSISTED MATLAB

This study aimed to compare the performance of a particular integral calculation using the Trapezoid and Gauss-Legendre method in five integral cases to determine the accuracy of the integral results value of both methods which are based on the relative error percentage. This study is a literature research which formulate mathematical problem that can be solved with the usual arithmetic operations or calculations which are addition, subtraction, multiplication and division to obtain numeral with the best accuracy. Trapezoidal method formula used is while the Gauss-Legendre formula used is , This study shows that the Gauss-Legendre method has better performance by giving the percentage of error which is relatively better than Trapezoid method used in the five cases. Keywords: Numerical Methods, Trapezoid method, the method of Gauss-Legendre

DYNAMIZATION OF THE TRAPEZOID METHOD FOR PLANAR POINT LOCATION IN MONOTONE SUBDIVISIONS

We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point location queries take O( log n) time, while updates take O ( log 2 n) time (amortized for vertex insertion/deletion and worst-case for the other updates). The space requirement is O(n log n). This is the first fully dynamic point location data structure for monotone subdivisions that achieves optimal query time.