Question

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

Answer 1

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

Answer 2

do you recognize this formula?

Answer 3

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

Answer 4

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

Answer 5

Pythagorean identity

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

Oh sec^2(x)!

Answer 10

yeppie!

Answer 11

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

Answer 12

Thank you so much! :)

Answer 13

np