A community for students.
Here's the question you clicked on:
 0 viewing
kirbykirby
 2 years ago
Integral! (related to gamma function maybe?)
\[\int\limits_{0}^{X}\frac{\lambda^3}{2}t^2e^{\lambda t}dt
kirbykirby
 2 years ago
Integral! (related to gamma function maybe?) \[\int\limits_{0}^{X}\frac{\lambda^3}{2}t^2e^{\lambda t}dt

This Question is Closed

kirbykirby
 2 years ago
Best ResponseYou've already chosen the best response.0Here it is: \[\int\limits_{0}^{X}\frac{\lambda^3}{2}t^2e^{\lambda t}dt\] I tried doing this trying to relate it to a gamma function but myupper bound is not infinity :S: \[=\frac{\lambda^3}{2}\int\limits_{0}^{X}t^2e^{\lambda t}dt\] \[Let : u=\lambda t =>t=u/t\]\[So: du=\lambda dt\]\[Bounds: u=0=>t=0 ; u=x=>t=x/\lambda\] \[\frac{\lambda^2}{2}\int\limits_{0}^{X/\lambda}(\frac{u}{\lambda})^2e^{u}du\]\[=\frac{1}{2}\int\limits_{0}^{X/\lambda}u^{31}e^{u}du\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1why do you not just use tabular method

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1it's a special type of by parts.. you can do by parts also

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1358916012425:dw

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1358916166540:dw

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[\int t^2e^{yt}=\frac{t^2e^{yt}}{y}\frac{2te^{yt}}{y^2}\frac{2e^{yt}}{y^3}+c\]

kirbykirby
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm interesting o_o!! As I was trying to do integration by parts, I realized I have to do it twice. Is this method related to doing int. by parts multiple times?

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=integral+of+t%5E2e%5E%7Byt%7D same answer as mine only simplified and yes Tabular method is when you have something of this sort \[\int t^nf(t)dt\] you take the derivatives of the t to thepower until you get to zero giving them alternating signs and integrate the f(t) one more time than how many it takes the t power function goes to zero

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1look up tabular method for a derivation of this

kirbykirby
 2 years ago
Best ResponseYou've already chosen the best response.0Oh wow this is quite neat !! :) thank you so much

kirbykirby
 2 years ago
Best ResponseYou've already chosen the best response.0I can't believe they never taught this technique..
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.