Virtual Labs

Which of the following functions can be approximated using Gauss Quadrature methods?

a: Any discontinuous function Explanation

Explanation

b: Any continuous function Explanation

Explanation

c: Only trigonometric functions Explanation

Explanation

d: Only polynomials Explanation

Explanation

The integration by Gauss quadrature methods using three points is given by

I \ = \ a\left(\frac{5}{9}f\left(a*\sqrt{\frac{3}{5}} + b \right) \ + \ \frac{8}{9}f(a*0 \ + \ b) \ + \ \frac{5}{9}f\left(-a*\sqrt{\frac{3}{5}} + b \right) \right) \

Explanation

I \ = \ a\left(\frac{9}{5}f\left(a*\sqrt{\frac{5}{3}} + b \right) \ + \ \frac{9}{8}f(a*0 \ + \ b) \ + \ \frac{9}{5}f\left(-a*\sqrt{\frac{5}{3}} + b \right) \right) \

Explanation

I \ = \ \frac{5}{9}f\left(a*\sqrt{\frac{3}{5}} + b \right) \ + \ \frac{8}{9}f(a*0 \ + \ b) \ + \ \frac{5}{9}f\left(-a*\sqrt{\frac{3}{5}} + b \right) \

Explanation

I \ = \ \frac{8}{9}f(a*0 \ + \ b)

Explanation

Integration - Gauss Quadrature Methods 3 Points