LaPlace Transform Calculation

[G. Cook]

I know that Prime has a LaPlace() command to find the transform of a f(t). But, when I attempt to find the classical definite integral of 0 to infinity of e^-s*t*sin(a*t)dt the answer comes back "undefined" When I do an indefinite integral of the same and try to take a limit as the t goes to infinity, I again get an "undefined". Of course, the limit when t goes to 0 results in the correct transform. My question is why is this is happening since Prime gives e^(minus infinity)=0 correctly. How can a transform be calculated using the classical integral definition on the Prime?



















0 =0 correctly. Secondly, How can one find a transform using the classical definition integral?

[Albert Chan]

(09-14-2021 09:16 PM)G. Cook Wrote:  integral of 0 to infinity of e^-s*t*sin(a*t)dt the answer comes back "undefined"

You need to give information about s, so that term e^(-s*t) is decaying

CAS> assume(s > 0)
CAS> int(e^(-s*t)*sin(a*t), t, 0, ∞)       → a/(a^2+s^2)

[G. Cook]

Thanks Albert: But on my Prime the CAS> int() function returns a definite integral symbol not the spelled out phrase you indicated. On my Prime, the filled out integral symbol still produces "undefined". My Prime version is 2.0.0.138659 (2018 08 02)

[Albert Chan]

Perhaps it is the typo of your integrand ?

"e^-s*t*sin(a*t)" should be "e^(-s*t)*sin(a*t)"

[Stevetuc]

(09-14-2021 10:40 PM)G. Cook Wrote:  Thanks Albert: But on my Prime the CAS> int() function returns a definite integral symbol not the spelled out phrase you indicated. On my Prime, the filled out integral symbol still produces "undefined". My Prime version is 2.0.0.138659 (2018 08 02)

Did you precede the integral with assume(s > 0) ?