# Gaussian Quadrature

Not what you're looking for? Search our solutions OR ask your own Custom question.

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 )

which is exact for all polynomial of degree ≤ 3, set up a system of four equations with unknown w1, w2, x1, x2 and find the values

Â© BrainMass Inc. brainmass.com September 26, 2022, 9:50 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/gaussian-quadrature-37586

#### Solution Preview

Solution:

We need to find two unknowns, the weight and the node ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer Gaussian Quadrature problems.

$2.49