There is a theorem for every major numerical integration technique that gives the error bound. ES is the symbol which is used to denote the error bound for Simpson's rule. The simplest numerical and most efficient approximations to the integral are the trapezoidal and Simpson approximations. Use our online error bound calculator for simpson's rule to find the error bound of an integral by providing the upper bound, lower bound and approximately function power 4.
Using Simpson's rule, find int(sin(x2),x = 0 .. 1) to within an accuracy of 10(-4).
|Error| ≤ ((b - a)5M) / (180 x n4))
|Error| ≤ ((1 - 105 × 30) / (180 x n4))
n = ((1 - 105 × 30) / (180)(1/4)