Trigonometric Integral sanity check

[Liquid7800]

Homework Statement

Hello,

After some algebraic manipulation my arc length formula of sqrt(1+y')^2) resulted in
sqrt(1+ tan^2 (x))...which can translate into sqrt(sec^2(x)).

My question is does the square root cancel the sec^2 ? becoming sec x?

Like sqrt(x^2) is x?


Thanks!

Homework Equations

The Attempt at a Solution

 

[Dick]

The sqrt(x^2) isn't x, it's |x|. And there are certainly cases where you can't throw the absolute value away. Be conscious of the sign of the expression you pulled out of the sqrt, or you might get a negative arc length or cancellation between different parts of the arc.

 

[Liquid7800]

Oh I see what you mean, for instance when integrating with respect to the bounds of the definite integral.
I think I am Ok, because my bounds are 0 -> pi/3 and my arc is in the fourth quadrant with respect to x.
Thanks for the answer...and you are absolutely right it is |x|...my mistake