Thread: Integral problem from Hardy book #2

I have no idea how to start to solve it.


Thank you...

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

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

Gaussian Quadrature -- from Wolfram MathWorld

The gaussian quadrature approximate a definite integral as...

(1)

... where the 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