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agentx5
Group Title
Check my work on this please? :)
Surface integral for the parametric equations
x = 4 + te\(^t\), y = (t\(^2\) + 1)e\(^t\), 0 ≤ t ≤ 3
Reference:
Surface Area = \(\large\int\limits_{a}^{b} 2\pi\ y\ ds \)
ds for parametric = \( \large\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt \)
So...
\[S.A. = \large\int\limits_{a}^{b} 2\pi\ ((t^2+1)e^t) \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt \]
\(dx = te^t\ dt\)
\(\large\frac{dx}{dt} = te^t\)
\(dy = (t^2+1)e^t+e^t(2t)\ dt \)
\(\large\frac{dy}{dt} = e^t(t^2+2t+1) \)
\(\large\frac{dy}{dt} = e^t(t+1)^2 \)
 2 years ago
 2 years ago
agentx5 Group Title
Check my work on this please? :) Surface integral for the parametric equations x = 4 + te\(^t\), y = (t\(^2\) + 1)e\(^t\), 0 ≤ t ≤ 3 Reference: Surface Area = \(\large\int\limits_{a}^{b} 2\pi\ y\ ds \) ds for parametric = \( \large\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt \) So... \[S.A. = \large\int\limits_{a}^{b} 2\pi\ ((t^2+1)e^t) \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt \] \(dx = te^t\ dt\) \(\large\frac{dx}{dt} = te^t\) \(dy = (t^2+1)e^t+e^t(2t)\ dt \) \(\large\frac{dy}{dt} = e^t(t^2+2t+1) \) \(\large\frac{dy}{dt} = e^t(t+1)^2 \)
 2 years ago
 2 years ago

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agentx5 Group TitleBest ResponseYou've already chosen the best response.0
\[\large\int\limits_{0}^{3} 2\pi\ ((t^2+1)e^t) \sqrt{(te^t)^2+(e^t(t+1)^2)^2}\ dt\] \[\large\int\limits_{0}^{3} 2\pi\ ((t^2+1)e^t) \sqrt{e^{2t}(t+1)^2+e^{2t}(t+1)^4}\ dt\] \[\large\int\limits_{0}^{3} 2\pi\ e^{2t}(t^2+1) \sqrt{t^2+2t+2}\ dt\] I'm getting 35833.252388 as the answer, Wolfram says that's ok so I'm looking for a setup error. Help? http://www.wolframalpha.com/input/?i=integrate+from+0+to+3+for+2pi%28e^%282t%29%29%28t^2%2B1%29sqrt%28t^2%2B2t%2B2%29
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
I'll have to leave soon unfortunately, but I wanted to get this up before I left because it can take several hours for these hard types of questions to be answered typically :D Hopefully I don't have any glaring errors >_<
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
Well actually I hope the error can be found, so the correct answer can be found
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
revolving to xaxis yes.
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
^_^ ty all in advance
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
Yes sir that is correct, xaxis rotation. That wasn't in the question's specific directions, but it was in the section's directions. Sorry about that. :/
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
"...the surface obtained by rotating the given curves about the xaxis."
 2 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.0
your dx/dt is wrong. Look at it again.
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
The 4 goes to 0, yes?
 2 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.0
Yes and in total, dx/dt = (t+1)e^t
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1341528724406:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
dw:1341528864848:dw
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
there is no close solution for integral.
 2 years ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.1
So your answer isn't correct.
 2 years ago
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