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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...
\[S.A. = \large\int\limits_{a}^{b} 2\pi\ ((t^2+1)e^t) \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt \]
\(dx = te^t\ dt\)
\(\large\frac{dx}{dt} = te^t\)
\(dy = (t^2+1)e^t+e^t(2t)\ dt \)
\(\large\frac{dy}{dt} = e^t(t^2+2t+1) \)
\(\large\frac{dy}{dt} = e^t(t+1)^2 \)
 one year ago
 one year ago
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... \[S.A. = \large\int\limits_{a}^{b} 2\pi\ ((t^2+1)e^t) \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt \] \(dx = te^t\ dt\) \(\large\frac{dx}{dt} = te^t\) \(dy = (t^2+1)e^t+e^t(2t)\ dt \) \(\large\frac{dy}{dt} = e^t(t^2+2t+1) \) \(\large\frac{dy}{dt} = e^t(t+1)^2 \)
 one year ago
 one year ago

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agentx5Best 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
 one year ago

agentx5Best 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 >_<
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
Well actually I hope the error can be found, so the correct answer can be found
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
revolving to xaxis yes.
 one year ago

agentx5Best 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. :/
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
"...the surface obtained by rotating the given curves about the xaxis."
 one year ago

JamesJBest ResponseYou've already chosen the best response.0
your dx/dt is wrong. Look at it again.
 one year ago

JamesJBest ResponseYou've already chosen the best response.0
Yes and in total, dx/dt = (t+1)e^t
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1341528724406:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
dw:1341528864848:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
there is no close solution for integral.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.1
So your answer isn't correct.
 one year ago
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