I have no idea how to start to solve it.

Thank you...

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- Jun 20th 2010, 09:52 AMAlso sprach ZarathustraIntegral problem from Hardy book #2
I have no idea how to start to solve it.

Thank you... - Jun 20th 2010, 10:06 AMroninpro
The first thing that comes to mind is using force. Did you try it?

- Jun 20th 2010, 11:13 AMchisigma
Probably it is a particular application of gaussian quadrature...

Gaussian Quadrature -- from Wolfram MathWorld

The gaussian quadrature approximate a definite integral as...

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

... where the $\displaystyle x_{k}$ 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

$\displaystyle \chi$ $\displaystyle \sigma$