Question

By using the Gaussian quadrature with 3 nodes from Table 6.1, estimate the following integral 1 Write down the quadrature rule that is applied to the above integral and report your computer result

Answer 1

The rule used is:

${\displaystyle \int _{a}^{b}f(x)\,dx\approx {\frac {b-a}{2}}\sum _{i=1}^{n}w_{i}f\left({\frac {b-a}{2}}x_{i}+{\frac {a+b}{2}}\right).}$ where

f(x) = 1r2

For are the weights and nodes

5 5 n-3, w1-w3

So that we have:

35 0 5 5 6 2 4 1 0

Which comes out to be:

5dr ะ 3.1411 1+x2 о