In 2001, the Borwein brothers studied the following integrals, which now bear their name
These integrals are remarkable because the first ones are all equal to π/2 . An obvious conjecture would be that this is true for every value.
Some decades ago, an old-school mathemacian would have had to hand-calculate the values of the first integrals (which would take several months, or even years), then assume all the integrals are equal to π 2 , and finally try and demonstrate this conjecture.
Today, we can use numerical calculus to evaluate as many of these integrals as possible before getting into a demonstration; this is the goal of this project.
You have to compute Borwein integrals, using the midpoint rule, the trapezoidal rule and the Simpson’s rule, and print both the value of In and the absolute difference between In and π/2 .
See the subject for further details !
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Grade : B | Mark : 20
| Category | Percentage | Tests | Crash ? |
|---|---|---|---|
| Simpson | 100% | 4/4 | x |
| Basic | 100% | 3/3 | x |
| Midpoint | 100% | 4/4 | x |
| Rigor | 100% | 5/5 | x |
| Trapezoidal | 100% | 4/4 | x |
| End scores | 100% | 20/20 | No |
- Boole's rule
- Simpson 3/8
Made with Quentin TREHEUX (LuciferBahamut)
Beware of -42 Epitech students !!!