Numerical Method20795 marksNumerical: Gaussian integration formulaGaussian integration algorithm
What is Gaussian integration formula? Evaluate the following integration using Gaussian integration three ordinate formula.
What is Gaussian integration formula? Evaluate the following integration using Gaussian integration three ordinate formula. $$\int_{0}^{1} \frac{\sin x}{x} dx$$ [5]
- Integral: $\int0^1 \frac{\sin x}{x},dx$ - Limits: $a=0$, $b=1$ - Method: Gauss-Legendre three-ordinate (n = 3) formula Three-point Gauss-Legendre nodes and weights: - $t1 = -\sqrt{3/5} = -0.7745967,\ w1 = 5/9$ - $t2 = 0,\ w2 = 8/9$ - $t3 = +\sqrt{3/5} = +0.7745967,\ w3 = 5/9$ Gauss-Legendre qu...