Condition based integration in MatLab

I have an integration : Int(rp.^2.*G(r,rp)*drp) where the integration is with respect to rp and the limit is on rp : 0->inf and G(r,rp) = 1/r for r>rp and G(r,rp)=1/rp for r<rp How to implement this integral in MatLab.

[David Goodmanson]

Hi pritha,

For large rp the integral goes like

Int G(r,p) rp^2 drp = Int (1/rp) rp^2 drp = Int rp drp 

and unfortunately, since the upper limit for rp is infinity, this integral diverges.

[pritha]

Hi David,

Thank you for your reply. If i consider the upper limit as 15-20? How will it be constructed in MatLab?

Answer 1

[Torsten]

syms r R rp real positive
G(r,rp) = piecewise(r<rp,1/rp,r>=rp,1/r);
int(rp^2*G(r,rp),rp,0,R)

ans = 

[pritha]

Thank you so much for your response. It helps me a lot.

[Torsten]

The extra distiction for R = r is not necessary since r^2/2 - r^2/6 = r^2/3, thus the formula for r < R will still be valid for r <= R.

[pritha]

Hi Torsten,

I have a doubt regarding the limit in this problem. Here the limit is given as (0,Inf). Is it possible to handle this limit in this problem?

[Torsten]

If r is fixed and R -> Inf, you see from the integration result that the second case (r<R) is the relevant one, and the result is - as already answered by @David Goodmanson - lim(R->Inf) (R^2/2-r^2/6) = Inf

syms r rp real positive
G(r,rp) = piecewise(r<rp,1/rp,r>=rp,1/r);
int(rp^2*G(r,rp),rp,0,Inf)

ans = 

∞

[pritha]

Thanks a lot.