Re-integration problem of abstract function
04-11-2019, 12:44 PM
Post: #1
 yangyongkang Member Posts: 51 Joined: Dec 2018
Re-integration problem of abstract function
Recently I tried to solve the re-integration of some abstract functions with xcas and found some problems.for example:
Code:
diff(integrate(integrate(f(sqrt(x^2+y^2)),y,-(sqrt(t^2-x^2)),sqrt(t^2-x^2)),x,-t,t),t)
Code:
 2pi*diff(f(t),t)*t
But the answer given by XCAS
Code:
 "Integral in limit not implemented yet Error: Bad Argument Value"

Related issues
Code:
∫(∫(e^(-(x^2+y^2)/2),y,-(sqrt(a^2-x^2)),sqrt(a^2-x^2)),x,-a,a)
Code:
integrate(sqrt(pi)*1/(sqrt(2))*erf(sqrt(a^2-x^2)*exp(ln(2)/2)/2)*exp(-x^2/2)-sqrt(pi)*1/(sqrt(2))*erf(-sqrt(a^2-x^2)*exp(ln(2)/2)/2)*exp(-x^2/2),x,-a,a)

In fact, we can get the correct answer through polar transformation.
Code:
∫(∫(e^(-r^2/2)*r,r,0,a),x,0,2π)
Code:
2*pi*(-exp(-a^2/2)+1)

Looking forward to the update of hp prime firmware in 2019

study hard, improve every day
04-25-2019, 12:20 PM
Post: #2
 yangyongkang Member Posts: 51 Joined: Dec 2018
RE: Re-integration problem of abstract function
Let's take a look at this issue.

study hard, improve every day
04-30-2019, 07:30 PM
Post: #3
 Eddie W. Shore Senior Member Posts: 1,606 Joined: Dec 2013
RE: Re-integration problem of abstract function
My only suggestion is to try integration and differentiation one step at a time (inside out). Patience may be needed.

I don't know if turning complex mode off in CAS would help.

Eddie.
04-30-2019, 08:25 PM
Post: #4
 Hans S. Member Posts: 56 Joined: Aug 2017
RE: Re-integration problem of abstract function
(04-11-2019 12:44 PM)yangyongkang Wrote:  Recently I tried to solve the re-integration of some abstract functions with xcas and found some problems.for example:
diff(integrate
brings to mind chinese figure skaters (f.) or the so-called pianist lang lang: indefinite exercise, no (artistic) result.

H.
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