1. Consider approximating integrals of the form
I ( f ) = ∫ √x f(x)dx
in which f(x) has several continuous derivatives on [0, 1]
a. Find a formula
∫ √x f(x)dx ≈ w1 f(x1) ≡ I1( f )
which is exact if f(x) is any linear polynomial.
b. To find a formula
∫ √x f(x)dx ≈ w1 f(x1) + w2 f(x2) ≡ I2( f )
We need to find two unknowns, the weight and the node ...
This solution is comprised of a detailed explanation to answer Gaussian Quadrature problems.