Thread: Integral of sqrt(1 + (cosx) ^ 2) ?

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

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

2. Originally Posted by parkhid

$
\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?

3. 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 : $\int\sqrt{1+y'^2}dx$

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

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

Iam very Now . what is ellipitic integral ??????

4. 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 : $\int\sqrt{1+y'^2}dx$

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

$\int\sqrt{1+cos^2x}dx$
Well, as you can see, it can't be done using a finite number of elementary functions.

5. Is There any other way to solve ?

6. it's been asnwered before.

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integrate sqrt 1 ( cosx)^2

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