The trapezoidal rule is one of the families of formulas used for numerical integration usually introduced during first-year calculus. In the field of mathematics involving statistical analysis, the trapezoidal rule is a technique that is utilized to approximate values of definite integrals. The key to implementing trapezoidal rule calculator is assuming the area of the integral, ie. the area under the graph to be a trapezoid.
Assuming the area under the graph to be a trapezoid, the approximate value of the integral can be calculated using the following formula:
For a more accurate approximation, partitioning of the integral sum can be done, and then the trapezoidal rule can be applied to each subinterval and finally summed to obtain the result.
This rule is an approximate method to find the value of definite
integrals, thus introducing some minor errors in our results. For
finding errors in the approximation, we need to find an upper bound
on the second derivative throughout integration, which is a hectic
task. However, with time, graphing devices such as a graphing
calculator has been developed which can be used easily by anyone to
find the upper bound and hence estimate the approximate error of
Trapezoidal rule error is of high importance. It can be calculated using the given formula: