Main presenter			Co-presenter(s)
Name :	Dr. Giora Mann		Name:	Dr. Nurit Zehavi
E-mail:	giorama@macam.ac.il		E-mail:	nurit.zehavi@weizmann.ac.il
Institution or Company:	Levinsky College of Education		Name:
Department:	Mathematics		E-mail:
City:	Beit Chanan		Name:
State/Province:			E-mail:
Country:	Israel		Name:
Type of presentation:	Lecture :  25 minutes.		E-mail:
Conference strand and number:	Derive & TI-CAS  ,    Number: D14		Schedule:   Room:	Friday, 12h00   1350
Related website:
Title of presentation:	Quadratic Approximations for Integration
Abstract:
The motivation for this paper originated from comments of curiosity by high school students while learning to compute definite integrals in a CAS environment. It is "surprising" that the area under the graph is not affected by the behavior of the function and its derivative inside the interval; it depends only on the values of the primitive function at the end-points of the integration interval. When using Derive to compute standard definite integrals, it was evident that approximating the exact result and approximating the integral itself yield different results. How does Derive do it? This question is even more relevant when we want to compute the length of almost any function. To satisfy students' curiosity we approximated the integrand by a quadratic function as a mean to estimate the definite integral. Surprisingly, the final approximation does not use the coefficients of the quadratic approximation; only three values of the integrands are involved. The road to Simpson's rule was opened when the approximation method was refined by refining the partition of the interval.