6.1.3-Numerical Integration: Newton-Cotes Integration Formulas Overview

[@ponnappabheemaiahmeederira5385]

So What is the maximum degree of polynomials (n) for which the Newton-Cotes formula can give the exact solution?

[@kvyi]

None. This is a numerical method and will only ever give an approximate solution.

[@romankral7232]

@@kvyi Actually, Simpson rule gives you exact solution if its used on polynomal function degree 3.

[@nimnim5149]

depends on the newton cotes formula we are using ... the trapezoidal will give exact solution if the function we are trying to integrate is a linear polynomial i.e a first degree polynomial , similarly the simpson 1/3 rule will give exact solution for the quadratic polynomial and simpson 3/8 rule will give exact solution for cubic polynomial.his is a numerical method and will only ever give an approximate solution. and the reason behind this is the uniqueness theorem of polynomials ... you can look it up yourself ...

[@nimnim5149]

@@kvyi no no the numerical methods do actually gives the exact solutions in some cases ... for example in N(th) degree gaussian quadrature we get exact solution for up to the polynomials of degree 2N+1

[@perlyax]

Nice Introduction!!