Different values of Gaussian Integration in Pracma library in R

I want to construct a gauss integration for the weight function:

$$w(x) = x^{1/2}$$ $in(0,1)$ of the form:
$$int_{0}^{1}x^{1/2}f(x)dx = w_{1}f(x_{1})+w_{2}f(x_{2})$$
begin{align*}
w_{1}+w_{2} =& int_{0}^{1}x^{1/2}cdot 1 dx = frac{2}{3}
w_{1}x_{1}+w_{2}x_{2}=&int_{0}^{1}x^{1/2}cdot x dx =frac{2}{5}
w_{1}x_{1}^2+w_{2}x_{2}^2=&int_{0}^{1}x^{1/2}cdot x^2 dx =frac{2}{7}
w_{1}x_{1}^3+w_{2}x_{2}^3=&int_{0}^{1}x^{1/2}cdot x^3 dx =frac{2}{9}
end{align*}

Solving the homogeneous system of 4 linear equations we get the solutions:

$$w_{1,2}=frac{1}{3} pm frac{sqrt{frac{7}{10}}}{15}$$
$$x_{1,2}=frac{5}{9} pm 2 frac{sqrt{ frac{10}{7} }}{9}$$

Therefore we have that : $$frac{1}{3} + frac{sqrt{frac{7}{10}}}{15} cdot f left(frac{5}{9} + 2 frac{sqrt{ frac{10}{7} }}{9}right) + frac{1}{3} – frac{sqrt{frac{7}{10}}}{15} cdot f left(frac{5}{9} – 2 frac{sqrt{ frac{10}{7} }}{9}right) = 0.54$$
but in R (pracma library)i get a different result:

library(pracma)
f = function(x)  x^(1/3)
integrate(f,0,1)
cc <- gaussLegendre(2, 0, 1);cc
Q <- sum(cc$w * f(cc$x))
Q

Q = 0.75 with different values of $x_{1,2}$ and $w_{1,2}$
Why what I am doing wrong?