Condition based integration in MatLab
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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.
2 个评论
David Goodmanson
2024-1-7
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
2024-1-7
采纳的回答
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)
5 个评论
pritha
2024-1-7
Torsten
2024-1-7
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
2024-1-10
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)
pritha
2024-1-10
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