Abstract:
Integration is one of the basic operation in mathematical calculus. It occurs in
almost all physical situations where the variable is continuous function of one or
more continuous independent variables. When the function is not continuous or if
the integrand, the function which is to be integrated, is not integrable using the
available techniques, we usually go for numerical techniques of integration. This
means that we have to apply numerical methods in order to get an approximate
solution. From the several numerical integration approaches, we proposed Line
Integrals Through Higher Degree Taylor Polynomial Approximation. Main
objective of our work is finding better approximation in terms of accuracy and to
derive a formula for error upper bound. We performed out work on algebraic,
exponential and trigonometric functions. At the end we compared our results with
some of the existing approximation methods such as Midpoint rule, Simpson’s
rule, Trapezoidal rules and Tangent line approximation and we proved our method
gives more accurate solution for those functions.
