Evaluation Of Double Intergral Using Trapezium Rule

If we use the composite trapezium rule in both the directions, we obtain

.......................1.5

If M = N = 1, we get the method given in (1.4).

                   Figure : 1.3 Weights in the trapeziumrule                                                                            Figure : 1.4 Weights in the trapezium rule.

For M = N = 2, the weights in the formula are given in Figure 1.3

For M = N = 4, the weights in the formula are given in Figure 1.4

Note :

The order of the composite trapezium rule is 1, that is, it integrates exactly polynomials of degree ≤1, in x and y. If we use the same mesh lengths along x and y directions, that is, h = k, then Romberg extrapolation can also be used to improve the computed values of the integral. The Romberg formula is same.