04-11-2019, 12:44 PM
Recently I tried to solve the re-integration of some abstract functions with xcas and found some problems.for example:
The answer we want is
But the answer given by XCAS
Related issues
The answer from XCAS
In fact, we can get the correct answer through polar transformation.
Get the answer
Looking forward to the update of hp prime firmware in 2019
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
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