# Math Help - Integral problem from Hardy book #2

1. ## Integral problem from Hardy book #2

I have no idea how to start to solve it.

Thank you...

2. The first thing that comes to mind is using force. Did you try it?

3. Probably it is a particular application of gaussian quadrature...

Gaussian Quadrature -- from Wolfram MathWorld

The gaussian quadrature approximate a definite integral as...

$\displaystyle \int_{a}^{b} f(x)\cdot dx \approx \sum_{k=1}^{n} a_{k} \cdot f(x_{k})$ (1)

... where the $x_{k}$ are the zeroes of the Legendre polynomial of degree n. An interesting property of the gaussian quadrature is that the error vanishes if f(*) is a polynomial of degree less or equal to 2n-1, and that situation is achieved if n=3 and f(*) is a polynomial of degree 5 or less...

Kind regards

$\chi$ $\sigma$