integral - Integration of 0-th order Bessel function using MATLAB -


i have simple question. i'm trying evaluate improper integral of 0th order bessel function using matlab r2012a:

v = integral(@(x)(besselj(0, x), 0, inf)

which gives me v = 3.7573e+09. should v = 1 in theory. when i'm trying 

v = integral(@(l)besselj(0,l), 0, 1000)

it results v = 1.0047. briefly explain me, going wrong integration? , how integrate bessel-type functions?

from docs improper integral on oscillatory function:

q = integral(fun,0,inf,'reltol',1e-8,'abstol',1e-13)

in docs example is

fun = @(x)x.^5.*exp(-x).*sin(x);

but guess in case try:

q = integral(@(x)(besselj(0, x),0,inf,'reltol',1e-8,'abstol',1e-13)

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