Numerically approximate ∫_a^b f(x)dx using Simpson's 1/3 rule: h/3 × [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + ... + f(x_n)] (n must be even). Error O(h^4) is much better than the trapezoidal rule.
| Constant | Symbol | Value |
|---|---|---|
| Speed of light | c | 2.99792458×10⁸ |
| Planck's constant | h | 6.62607015×10⁻³‴ |
| Boltzmann constant | kʙ | 1.380649×10⁻²³ |
| Avogadro's number | Nₐ | 6.02214076×10²³ |
| Gravitational constant | G | 6.6743×10⁻¹¹ |
| Gas constant | R | 8.31446 |
| Elementary charge | e | 1.602176634×10⁻¹⁹ |
| Electron mass | mₑ | 9.1093837015×10⁻³¹ |
| Proton mass | mₚ | 1.67262192369×10⁻²⁷ |
| Fine-structure constant | α | 7.2973525693×10⁻³ |
Numerically approximate ∫_a^b f(x)dx using Simpson's 1/3 rule: h/3 × [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + ... + f(x_n)] (n must be even). Error O(h^4) is much better than the trapezoidal rule
Each component has a specific meaning:
Note: Interpret the simpson's rule result against the thresholds and context described above.
Enter the Simpson's 1/3 rule: h/3 × [f + 4f + 2f + 4f + for the scenario you are assessing. Numerically approximate ∫_a^b f(x)dx using Simpson's 1/3 rule: h/3 × [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + ... + f(x_n)] (n must be even). Error O(h^4) is much better than the trapezoidal rule. Use the simpson's rule result to inform your calculation.