'2. Evaluate the following integral with (a) Romberg integration (€ 0.5%) , (b) the two-point Gauss quadrature formula'
Added by Daniel W.
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Evaluate the following integral a) analytically, b) Romberg integration (εs = 0.5%), c) the three-point Gauss quadrature formula, I = ∫₀⁸ (-0.045x⁴ + 0.74x³ - 5x² + 7.1x + 3)dx
Sri K.
(a): Use Gauss Quadrature to evaluate the integral of f(x) = 0.2 + 25x - 200x^2 + 675x^3 - 900x^4 + 400x^5 between the limits x = 0 to x = 0.8 with n = 2. (b): Use a Legendre interpolating polynomial to evaluate f(2) from the given data: x : 1 4 6 f(x) : 0 1.386294 1.791760
Adi S.
2. a) Use Romberg Integration to approximate R3,3 for the integral ∫[3 to 3.5] x/√(x^2-4) dx b) Romberg Integration for approximating ∫[0 to 1] f(x)dx gives R1,1 = 4 and R2,2 = 5. Find f(1/2) 3. Use Gaussian Quadrature Integration with n=3 to approximate the following integrals a) ∫[1 to 1.6] 2x/(x^2-4) dx b) ∫[0 to π/4] x^2 sin x dx
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