Proof of Laplace Transform of T^n | L[T^n] | Power Function

In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace, is an integral transform that converts a function of a real variable to a function of a complex variable s. The transform has many applications in science and engineering because it is a tool for solving differential equations.
In this video, we are going to learn how to proof the Laplace Transform of the power function.
we are to learn how to solve for the Laplace Transform of t^n. L{t^n}.
There's a shorter way to prove this, learn it here.
To watch more videos on Laplace Transform, click;
• Laplace Transform | Si...
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[@josephmutunga6923]

This is incredible 🎉🎉🎉you have my subscription already
Continue sharing more... Thank you

[@AVITECHNOLOGIES]

You're are welcome.
I'm glad to have you here 😊

[@josephmutunga6923]

@@AVITECHNOLOGIES please do a video on simultaneous differential equations using laplace transform

[@AVITECHNOLOGIES]

@josephmutunga6923 okay. I'll make a video on it next Month

[@oulafatla8686]

Thank you so much for sharing the video

[@Tojanplayz]

Good work man

[@latsubless1773]

I love your explanation to this problem

[@AVITECHNOLOGIES]

Thanks

[@joxtimes]

Thank you very much Sir for helping me, Love you from India

[@AVITECHNOLOGIES]

One Love
You're welcome

[@heza-ssa]

perfect thanks

[@AVITECHNOLOGIES]

You're welcome

[@imafidonerisson5527]

Nice one

[@angeljoyadackaparayil8096]

❤

[@Tojanplayz]

Isnt it suppose to be I^n+1?

[@Tojanplayz]

Hello sir pls reply

[@esenemichael5477]

Can we be asked to prove this standard transforms in the exam?

[@AVITECHNOLOGIES]

Yes sir, in short, it is a past question.
The Laplace Transform of t to the nth power, is one of the many transforms asked to be proved.
Thanks.

[@siawjohn]

What if we proceeded with integration by part on the second time so that we'll have both of them equal

[@AVITECHNOLOGIES]

@@siawjohn well, I think that's possible, but that's time consuming because we can clearly use reduction formulas to proceed.

[@siawjohn]

@AVITECHNOLOGIES okay sir

[@siawjohn]

Sir, do you have any channel a student can communicate with you on?

[@AVITECHNOLOGIES]

@@siawjohn WhatsApp.
My number is on my bio/profile.
Same with my email.

[@sharvilshah2448]

Why can't we put n=0 in 2 column formula of In ?

[@AVITECHNOLOGIES]

@@sharvilshah2448 I don't seem to get your question. Can you indicate the time stamp?

[@sharvilshah2448]

I was saying that why can't we put n=0 in formula at 9:59 to find I not​@@AVITECHNOLOGIES

[@AVITECHNOLOGIES]

@@sharvilshah2448 well, if you put n=0, what you're solving for is now I_0 and not I_n

[@sharvilshah2448]

So if we put n=0 at 9:59 then, we get I_0 = 0. So why is it not valid? Or am I wrong somewhere?

[@AVITECHNOLOGIES]

@sharvilshah2448 here's the error, n goes from 1 and above. That's when it works

[@fidelisomoni7537]

Jamb Students, oya sope otilor