Share
Explore BrainMass

GAUSSIAN NUMERICAL INTEGRATION

GAUSSIAN NUMERICAL INTEGRATION

1. Consider approximating integrals of the form...

in which f(x) has several continuous derivatives on [0, 1]
a. Find a formula... which is exact if f(x) is any linear polynomial.

b. To find a formula... which is exact for all polynomial of degree ≤ 3, set up a system of four equations with unknown w1, w2, x1, x2. Verify that...

Is a solution of the system. The verification can be numerical (say using Matlab) or symbolic (say using Maple or Mathematica).

c. Apply I1 and I2 to the evaluation of...

Please see attached.

Attachments

Solution Summary

This solution is comprised of a detailed explanation to solve gaussian numerical integration.

$2.19