Tabular integration is a method used to numerically approximate the value of a definite integral. It involves dividing the interval of integration into smaller subintervals and using the trapezoidal rule to estimate the area under the curve within each subinterval.
To perform tabular integration, the interval of integration is first divided into equally spaced subintervals. The trapezoidal rule is then used to calculate the area under the curve within each subinterval. Finally, the calculated areas are added together to approximate the value of the definite integral.
Tabular integration is a relatively simple and straightforward method for approximating definite integrals. It is also more accurate than other numerical integration methods, such as the midpoint rule or Simpson's rule, when the function being integrated is not smooth.
Tabular integration is limited by the number of subintervals that can be used to approximate the integral. If the interval of integration is too large or the function being integrated is highly oscillatory, the accuracy of the approximation may be reduced. In these cases, other numerical integration methods may be more suitable.
One way to check the accuracy of tabular integration results is to compare them to the exact value of the definite integral, if it is known. Another method is to use a smaller interval of integration and compare the results to the original approximation. Additionally, mathematical software or calculators can be used to perform the integration and compare the results to those obtained through tabular integration.