Repeat Example 8.7 for Gauss quadrature using Program 8.8.

Example 8.8

Use the multiple trapezoidal rule to determine how the error in the integral

depends on the number of trapezoids.

Example 8.7

To test our claim about the accuracy of these methods, use Program 8.4 to calculate the integral

which we know has the value I = 1 for any positive integer m.

Program 8.4

We can write a nice compact program that allows us to integrate some function f (x) using a particular order of the Newton–Coates formula by taking advantage of the switch operator, which is a useful alternative to implementing many if-else statements.

= 1/2 s xdx (8.4.8)