Question

Gaussian Quadrature Integration 1. Use Gaussian Quadrature Two point formula to approximate the integral $\int_0^1 x^2 e^{-x} dx$ (NOTE: $c_{21} = 1$, $c_{22} = 1$, $r_{21} = \frac{1}{\sqrt{3}}$, $r_{22} = -\frac{1}{\sqrt{3}}$) 2. Use Three-point Gaussian Quadrature to approximate $\int_0^{\pi/4} e^{3x} sin2 x dx$. (Use $c_{31} = \frac{5}{9}$, $c_{32} = \frac{8}{9}$, $c_{33} = \frac{5}{9}$, $r_{31} = -\sqrt{\frac{3}{5}}$, $r_{32} = 0$, $r_{33} = \sqrt{\frac{3}{5}}$). 3. Approximate $\int_0^2 x^2 e^{-x^2} dx$ by 3 point Gaussian Quadrature formula.

          Gaussian Quadrature Integration
1. Use Gaussian Quadrature Two point formula to approximate the integral
$\int_0^1 x^2 e^{-x} dx$
(NOTE: $c_{21} = 1$, $c_{22} = 1$, $r_{21} = \frac{1}{\sqrt{3}}$, $r_{22} = -\frac{1}{\sqrt{3}}$)
2. Use Three-point Gaussian Quadrature to approximate $\int_0^{\pi/4} e^{3x} sin2 x dx$.
(Use $c_{31} = \frac{5}{9}$, $c_{32} = \frac{8}{9}$, $c_{33} = \frac{5}{9}$, $r_{31} = -\sqrt{\frac{3}{5}}$, $r_{32} = 0$, $r_{33} = \sqrt{\frac{3}{5}}$).
3. Approximate $\int_0^2 x^2 e^{-x^2} dx$ by 3 point Gaussian Quadrature formula.

Gaussian Quadrature Integration
1. Use Gaussian Quadrature Two point formula to approximate the integral
∫0^1 x^2 e^-x dx
(NOTE: c21 = 1, c22 = 1, r21 = (1)/(√(3)), r22 = -(1)/(√(3)))
2. Use Three-point Gaussian Quadrature to approximate ∫0^π/4 e^3x sin2 x dx.
(Use c31 = (5)/(9), c32 = (8)/(9), c33 = (5)/(9), r31 = -√((3)/(5)), r32 = 0, r33 = √((3)/(5))).
3. Approximate ∫0^2 x^2 e^-x^2 dx by 3 point Gaussian Quadrature formula.

Added by Holly S.

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