# Integral of sqrt(1 + (cosx) ^ 2) ?

• Jun 2nd 2010, 05:21 AM
parkhid
Integral of sqrt(1 + (cosx) ^ 2) ?

$\displaystyle \int\sqrt{1+cos^2x}dx$
• Jun 2nd 2010, 05:29 AM
mr fantastic
Quote:

Originally Posted by parkhid

$\displaystyle \int\sqrt{1+cos^2x}dx$

integrate Sqrt&#x5b;1 &#x2b; &#x28;Cos&#x5b;x&#x5d;&#x29;&#x5e;2&#x5d; - Wolfram|Alpha

Where has the integral come from?
• Jun 2nd 2010, 05:36 AM
parkhid
The main question intend is to calculate the length of arc which

will create by F(x) = Sin(X) from 0 to pi .

so, we should calculate this : $\displaystyle \int\sqrt{1+y'^2}dx$

and if we put cosx instead of y' we have the above integral.

$\displaystyle \int\sqrt{1+cos^2x}dx$

Iam very (Nerd) Now . what is ellipitic integral ??????
• Jun 2nd 2010, 05:38 AM
mr fantastic
Quote:

Originally Posted by parkhid
The main question intend is to calculate the length of arc which

will create by F(x) = Sin(X) from 0 to pi .

so, we should caclculate this : $\displaystyle \int\sqrt{1+y'^2}dx$

and if we put cosx instead of y' we have the above integral.

$\displaystyle \int\sqrt{1+cos^2x}dx$(Nerd)

Well, as you can see, it can't be done using a finite number of elementary functions.
• Jun 2nd 2010, 05:43 AM
parkhid
Is There any other way to solve ?
• Jun 2nd 2010, 06:04 AM
Krizalid
it's been asnwered before.