Improper Integrals with the HP-15C LE & CE

[Valentin Albillo]

(11-19-2023 01:11 AM)Namir Wrote:  Yes the HP Prime in CAS mode gives the anwer of 2!

No need for the "!", Namir, any CAS that wouldn't instantly deliver the 2 result would be fit for the garbage bin, as this integral is but a case of f(x) = xⁿ for n = -1/2, which is as trivial to symbolically integrate as it gets, even by hand:

Integral of f(x) .dx = x^-1/2+1/(-1/2+1) + C = 2*Sqrt(x) + C.

and upon substituting the integration limits you get 2*Sqrt(1) - 2*Sqrt(0) = 2*1 - 2*0 = 2.

Regards.
V.