Find the exact length of the curve.
y = ln(sec x), 0 ≤ x ≤ π/4

Question

Find the exact length of the curve.
y = ln(sec x),   0 ≤ x ≤ π/4

freckles · Answer

$$\int\limits_{0}^{\frac{\pi}{4}}\sqrt{1+(y')^2} dx $$

freckles · Answer

do you recognize this formula?

anonymous · Answer

Yes! I'm just stuck trying to integrate $$\int\limits_{0}^{\pi/4} \sqrt{1+\tan^2} dx$$

freckles · Answer

what is 1+tan^2(x) 
think of an identity

freckles · Answer

Pythagorean identity

anonymous · Answer

these problems cooked to within an inch of their life
think of all the effort it took to make a problem where you could take the derivative, square it, add 1, take the square root, and then come up with something integrable
i tried it once, it took over half an hour
maybe over an hour

freckles · Answer

lol That is why I give up and only gave problems from the book as test questions

anonymous · Answer

i know right? i was kind of proud of myself when i was done

anonymous · Answer

Oh sec^2(x)!

freckles · Answer

yeppie!

freckles · Answer

and sec is positive on the interval 0 to pi/4
so sqrt(sec^2(x))=sec(x)

anonymous · Answer

Thank you so much! :)

freckles · Answer

np