Question

find the length of the curve:

y = ln(cos x) 0 14 years ago

Answer 1

\[s = \int\limits_0^{\frac{\pi}{3}} \sqrt{1+ |f'(x)|^2}dx = \int\limits_0^{\frac{\pi}{3}} \sqrt{1+ \tan(x)^2}dx = \log(2+\sqrt{3}) = 1.31\]

Answer 2

how'd you get log(2 + root3?

Answer 3

Right. Now, it's not obvious how you did the integration, although it is helps a lot to remember that
1 + tan^2 x = sec^2 x.

So you need the integral of sec x

Answer 4

right now i have the integral of (secx^2)^1/2

Answer 5

Which is sec x

Answer 6

the integral of sec?

Answer 7

\[\int\limits \sec x \ dx = \int\limits \frac{\sec x (\sec x + \tan x)}{\sec x + \tan x} \ dx\]

Answer 8

but its secx^2 not just sec x

Answer 9

No it's not. It is sec x, regardless of whatever notation cptnc used.

Answer 10

The sqrt cancels the ^2 out

Answer 11

oh duh!

Answer 12

okay so the answer is ln(2 + root3)