Question

Find the following integral

1J2(x)da

Answer 1

Here we will use a basic property of Bessel's function.

if denotes a Bessel function of order n.

J (r)

then ,

....................(i)

d (x J())x"Jn+1() dx

we have to evaluate ,

1J2(x)da

so, if we put n=1 in the above equation (i)

we get ,

d (J1())-x1J()

integrating , both sides with respect to x.

J2)da (J))d dr

as per second fundamental theorem of calculus, the integration cancels the derivative,

so,

J2(r)da J1()C-

C is the integration constant.

= -xJ ()C J2(x)d or

( is bessel function of order 1