Posted by **sammyg** on Tuesday, January 24, 2012 at 9:46pm.

Find the arc length of the graph of the function over the indicated interval. (Round your answer to three decimal places.)

y = ln (sin(x))

,[π/4,3π/4]

- calculus -
**Steve**, Wednesday, January 25, 2012 at 1:15pm
y = ln sinx

y' = 1/sinx * cosx = tanx

s = Int(sqrt(1+(y')^2)dx)[pi/4,3pi/4]

= Int(sqrt(1+tan^2(x))dx)[pi/4,3pi/4=

= Int(secx dx)[pi/4,3pi/4]

= ln|secx + tanx|[pi/4,3pi/4]

= ln|-1/√2 + 1| - ln|1/√2 + 1|

= ln|(1-√2/(1+√2)|

= ln|2√2-3|

= ln(3-2√2)

## Answer this Question

## Related Questions

- calculus - Find the arc length of the graph of the function over the indicated ...
- Math, please help - Which of the following are trigonometric identities? (Can be...
- Math integrals - What is the indefinite integral of ∫ [sin (π/x)]/ x^...
- Trig Help! - Question: Trying to find cos π/12, if cos π/6 = square ...
- Math - Evaluate *Note - We have to find the exact value of these. That I know to...
- Math - The null and alternate hypotheses are: H0: π1 ≤ π2 H1...
- calculus - Consider the given function and the given interval. f(x) = 4 sin x &#...
- calculus - Find the linearization of the function below at x = π/3.? y=sin(...
- Calculus - We can find some of the solutions of sin x = 0.2 graphically by ...
- calculus - Find the absolute maximum and absolute minimum values of f on the ...