In this thesis, the evaluation of integrals from zero to infinity involving product of a first kind Bessel function of integer order n with a function f is considered. The
evaluation of infinite integrals involving trigonometric or Bessel function kernels are not easy due to the oscillations in trigonometric or Bessel functions. In the past,
the method of dividing an oscillatory integral at its zeros, forming a sequence of partial sums, and using extrapolation techniques to accelerate convergence was found
to be the most efficient technique available. But, only the Bessel functions of order zero and one were considered. In this thesis, we follow the same procedure but
are able to obtain results for any order n. As extrapolation techniques we use Euler Method and Epsilon algorithm.The results obtained using these two methods
were compared. We also give a simple but very effective technique for calculating the zeros of a Bessel function.

Keywords : INFINITE INTEGRALS, BESSEL FUNCTIONS