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 w...

For Gauss quadrature we expect the integral to be exact up to a polynomial of order ...

Repeat Example 8.7 for Gauss quadrature using Program 8.8. Example 8.8 Use the multiple trapezoidal rule to

Question:

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 = 1/2 s xdx (8.4.8)

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 +Df xdx I = (m + 1) (8.3.22)

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 function out = integrate_Newton_Coates (a, b, n) % a = lower bound of integral 2 3 % b = upper bound of