Find length of the curve

y=ln(cosx) {x,0,pi/2}

I am stuck and I dont know how to integrate sqrt(sec^2).

My Work:

Attachment 15714

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- Mar 1st 2010, 04:25 PMracewithferrariFinding the are of the curve
Find length of the curve

**y=ln(cosx) {x,0,pi/2}**

I am stuck and I dont know how to integrate sqrt(sec^2).

My Work:

Attachment 15714 - Mar 1st 2010, 04:45 PMskeeter
- Mar 1st 2010, 05:48 PMracewithferrari
I do not get it about dropping the absolute value.

I know what the integral of sqrt(sec^2) is . But I know dont know how I will solve it comes to Exams. - Mar 2nd 2010, 06:46 AMskeeter
you say this in your original post ...

Quote:

I am stuck and**I dont know how to integrate sqrt(sec^2).**

Quote:

**I know what the integral of sqrt(sec^2) is.**But I know dont know how I will solve it comes to Exams.

here is the arclength calculation ...

$\displaystyle

\int_0^{\frac{\pi}{3}} \sec{x} \, dx

$

$\displaystyle \left[\ln(\sec{x} + \tan{x})\right]_0^{\frac{\pi}{3}}$

$\displaystyle

\left[\ln\left(\sec{\frac{\pi}{3}} + \tan{\frac{\pi}{3}}\right)\right] - \left[\ln\left(\sec{0} + \tan{0}\right)\right]

$

$\displaystyle

\left[\ln\left(2 + \sqrt{3}\right)\right] - \left[\ln\left(1+0\right)\right]

$

$\displaystyle

\ln(2 + \sqrt{3})

$