Evaluating Symbolic, Definite Integral with Bessel's Function

Hello,

I need to evaluate the following definite, symbolic integral with 0th order bessel function inside.

Where J0 is the 0th order bessel function and also a function of r and A(i) which is an array of integers. I need to evaluate the integral for each value of A(i) from i=1:5. Here is what I have so far:

syms r 
for i=1:5
    An(i)= int(20*besselj(0,A(i)*r)*r,0,3.1);
end

Matlab is able to evaluate this, but I am suspicious of the results as they don't make sense in the context of my problem. Does this seem like the correct approach?

[Walter Roberson]

syms A U
assume(U>=0)
syms r 
An = int(20*besselj(0,A*r)*r,0,U);

An

An = 

That looks appropriate to me.

Answer 1

[Torsten]

You might want to compare with the numerical solution:

An = integral(@(r)20*besselj(0,A.*r).*r,0,3.1,'ArrayValued',true)