Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

UnkleRhaukusBest ResponseYou've already chosen the best response.1
\[\begin{align*} \mathcal L\left\{e^{t^2}\right\}&= \int\limits_0^\infty e^{t^2}e^{pt}\cdot\text dt\\ &=\int\limits_0^\infty e^{t(p+t)}\cdot\text dt\\ \end{align*}\]
 one year ago

sthop456Best ResponseYou've already chosen the best response.0
I would think that any base, including e, when raised to a negative exponent, becomes a decay problem that approaches 0.
 one year ago

AccessDeniedBest ResponseYou've already chosen the best response.2
Maybe completing the square would be helpful? I did a similar problem (it was the only 'question' i asked) and it seemed to work out well for that one. http://puu.sh/1r1nO
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
\[\begin{align*} \mathcal L\left\{e^{t^2}\right\}&= \int\limits_0^\infty e^{t^2}e^{pt}\cdot\text dt\\ &=\int\limits_0^\infty e^{(t^2+pt)}\cdot\text dt\\ &=\int\limits_0^\infty e^{\left(t^2+pt+\left(\tfrac p2\right)^2\right)+\left(\tfrac p2\right)^2}\cdot\text dt\\ &=e^{\left(\tfrac p2\right)^2}\int\limits_0^\infty e^{\left(t+\tfrac p2\right)^2}\cdot\text dt\\ &=e^{\tfrac {p^2}4}\int\limits_0^\infty e^{\left(t+\tfrac p2\right)^2}\cdot\text dt\\ \text{let }t+\tfrac p2=w\\ \text dt=\text dw\\ t=0\rightarrow w=\tfrac p2\\ t=\infty\rightarrow w=\infty\\ &=e^{\tfrac {p^2}4}\int\limits_{\tfrac p2}^\infty e^{w^2}\cdot\text dw\\ &=e^{\tfrac {p^2}4}\left(\frac{\sqrt\pi}{2}\text{erfc}\left(\tfrac p2\right)\right)\\ &=\frac{\sqrt\pi}{2}e^{\tfrac {p^2}4}\text{erfc}\left(\tfrac p2\right)\color{red}\checkmark\\ \end{align*}\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
thankyou @AccessDenied
 one year ago

AccessDeniedBest ResponseYou've already chosen the best response.2
You're welcome! :)
 one year ago
See more questions >>>
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.