I'm having trouble with the following:(adsbygoogle = window.adsbygoogle || []).push({});

The problem is to find the arc length of the following parametric function:

x=(e^-t)(cos t), y=(e^-t)(sin t) from 0 to [tex] \pi [/tex]

I found that

[tex] \frac{\partial y}{\partial t} = e^{-t}(\cos{t}-\sin{t}) [/tex],

[tex] \frac{\partial x}{\partial t} = -e^{-t}(\sin{t}+\cos{t})[/tex]

Then setting up the integral:

[tex]\int_{0}^{\pi} \sqrt{(-e^{-t}(\sin{t}+\cos{t}))^2+(e^{-t}(\cos{t}-\sin{t}))^2} dt [/tex]

I then simplified the square root to;

[tex] e^{-2t}(-4\cos{t}\sin{t}))=e^{-2t}*{-2\sin{2t}} [/tex]

This makes the integral:

[tex] \int_{0}^{\pi} e^{-t}\sqrt{-2\sin{2t} dt[/tex]

Can this integral even be solved?

I don't think this problem was ment to be that difficult, so I think I made a mistake somewhere, but I can figure what.

Thanks!

Tom

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Arc length and parametric function

**Physics Forums | Science Articles, Homework Help, Discussion**