Question

The system egin{cases} w_0 + w_1 = 2 \ w_0x_0 + w_1x_1 = 0 \ w_0x_0^2 + w_1x_1^2 = frac{2}{3} \ w_0x_0^3 + w_1x_1^3 = 0 end{cases} arises in the determination of Gaussian rules for the numerical approximation of the integral int_{-1}^{1} f(x) dx by w_0f(x_0) + w_1f(x_1). a) [by hand] Write this system in the form F(x) = 0 using x = [x_0 x_1 w_0 w_1]^T (i.e., write w_0 = x_2 and w_1 = x_3).

          The system
egin{cases} w_0 + w_1 = 2 \ w_0x_0 + w_1x_1 = 0 \ w_0x_0^2 + w_1x_1^2 = frac{2}{3} \ w_0x_0^3 + w_1x_1^3 = 0 end{cases}
arises in the determination of Gaussian rules for the numerical approximation of the integral int_{-1}^{1} f(x) dx by w_0f(x_0) + w_1f(x_1).
a) [by hand] Write this system in the form F(x) = 0 using x = [x_0  x_1  w_0  w_1]^T (i.e., write w_0 = x_2 and w_1 = x_3).

$The system egincases w0 + w1 = 2 w0x0 + w1x1 = 0 w0x0^2 + w1x1^2 = frac23 w0x0^3 + w1x1^3 = 0 endcases arises in the determination of Gaussian rules for the numerical approximation of the integral int-1^1 f(x) dx by w0f(x0) + w1f(x1). a) [by hand] Write this system in the form F(x) = 0 using x = [x0 x1 w0 w1]^T (i.e., write w0 = x2 and w1 = x3).$

Added by Marcus R.

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