## agentx5 3 years 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... $S.A. = \large\int\limits_{a}^{b} 2\pi\ ((t^2+1)e^t) \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt$ $$dx = te^t\ dt$$ $$\large\frac{dx}{dt} = te^t$$ $$dy = (t^2+1)e^t+e^t(2t)\ dt$$ $$\large\frac{dy}{dt} = e^t(t^2+2t+1)$$ $$\large\frac{dy}{dt} = e^t(t+1)^2$$

1. agentx5

$\large\int\limits_{0}^{3} 2\pi\ ((t^2+1)e^t) \sqrt{(te^t)^2+(e^t(t+1)^2)^2}\ dt$ $\large\int\limits_{0}^{3} 2\pi\ ((t^2+1)e^t) \sqrt{e^{2t}(t+1)^2+e^{2t}(t+1)^4}\ dt$ $\large\int\limits_{0}^{3} 2\pi\ e^{2t}(t^2+1) \sqrt{t^2+2t+2}\ dt$ 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. agentx5

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 >_<

3. agentx5

Well actually I hope the error can be found, so the correct answer can be found

4. mahmit2012

revolving to x-axis yes.

5. agentx5

6. agentx5

Yes sir that is correct, x-axis rotation. That wasn't in the question's specific directions, but it was in the section's directions. Sorry about that. :-/

7. agentx5

"...the surface obtained by rotating the given curves about the x-axis."

8. JamesJ

your dx/dt is wrong. Look at it again.

9. agentx5

The 4 goes to 0, yes?

10. JamesJ

Yes and in total, dx/dt = (t+1)e^t

11. mahmit2012

|dw:1341528724406:dw|

12. mahmit2012

|dw:1341528864848:dw|

13. mahmit2012

there is no close solution for integral.

14. mahmit2012