Question 8.12: Use trap to find the integral using the tabulated data in Ta...
Use trap to find the integral using the tabulated data in Table 8.5.
| Table 8.5 Tabulated data for Example 8.12. | |||||
| 1 | 0.75 | 0.5 | 0.25 | 0 | x |
| 0.3679 | 0.5698 | 0.7788 | 0.9394 | 1 | y |
A MATLAB script to solve this problem is:
1 function matlab_trapz
2 y = [1.0000, 0.9394, 0.7788, 0.5698, 0.3679];
3 I = trapz(y)/4
Our data have a spacing Δx = 1/4, so we have to multiply the result from trapz by the spacing Δx. The data in Table 8.5 are simply the values of y = e^{−x^2} , so this problem is equivalent to solving Eq. (8.7.1). The result of the five-point multiple trapezoidal rule, I = 0.7430, is not so far from the result from Example 8.7.1, I = 0.7468.
I = ∫^1_0 e^{−x^2} dx (8.7.1)
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