CODEWITHSUNDEEP
wolfram-mathematicanumerical-integration
Cici
Cici

Reputation: 65

Mathematica: Integration of Bessel Function & Exponent Function & Trigonometric Function

I have an integral with the form

Int[k_]:=Integrate[Exp[-x]xSin[x]BesselJ[0,k*x],{x,0,10}]

where BesselJ[0,kr] is the modified Bessel function of the first kind.

Now i can't get the directly answer from Mathematica..

I want to get the curve of Int[k], maybe a approximate is also acceptable..What can I do then?

Upvotes: 1

Views: 1300

Answers (2)

vsoftco
vsoftco

Reputation: 56567

Since the function doesn't have an antiderivative, your best bet is to numerically integrate. Example:

Int[k_] := NIntegrate[Exp[-x] x Sin[x] BesselJ[0, k x], {x, 0, 10}]
Plot[Int[k], {k, -5, 5}]

enter image description here

PS: I have edited your question, as you had some typos. You cannot use I as the symbol (it messes the complex i), and also when defining a function have to use := instead of =.

Upvotes: 2

Chris Degnen
Chris Degnen

Reputation: 8655

Even setting the constants to unity, Mathematica cannot find a formula for the integral. I.e.

a = b = k = d = 1;

Integrate[(a r Exp[-r] - b r Sin[k (r - d)] Exp[-r]) BesselJ[0, k r], r]

The integral is returned unchanged.

Simplifying things a bit shows some progress, returning a formula.

Integrate[Sin[k (r - d)] BesselJ[0, k r], r]

But adding back in one of the exponents throws it again.

Integrate[Sin[k (r - d)] Exp[-r] BesselJ[0, k r], r]

Upvotes: 1

Related Questions