# calculus

posted by .

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 -

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)

## Similar Questions

1. ### Math integrals

What is the indefinite integral of ∫ [sin (π/x)]/ x^2] dx ?
2. ### calculus

Find the arc length of the graph of the function over the indicated interval. (Round your answer to three decimal places.) y = (2/3)x^(3/2) +7 ;[0,6]
3. ### Math

The null and alternate hypotheses are: H0: π1 ≤ π2 H1: π1> π2 A sample of 100 observations from the first population indicated that X1 is 70. A sample of 150 observations from the second population revealed …

Which of the following are trigonometric identities?
5. ### calculus

1. what trig function has an amplitue of 1 and negative values for angles between π/2 and π?
6. ### math

Find the area of the region. (Round your answer to three decimal places.) between y = cos t and y = sin t for −π/2 ≤ t ≤ π/2
7. ### Trigonometry

Use a graph of the function to approximate the solution of the equation on the interval [−2π, 2π]. (List the solutions in increasing order from left to right on the x-axis. Round your answers to three decimal places.)
8. ### Trigonometry

Use a graph of the function to approximate the solution of the equation on the interval [−2π, 2π]. (List the solutions in increasing order from left to right on the x-axis. Round your answers to three decimal places.) …
9. ### Pre-Cal

An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 2 cos 2θ − 1 = 0 a). Find all solutions of the equations …
10. ### Pre-Cal:(Cont.)

[Note: I've tried this problem 4 times already and still have it wrong. I know the steps to doing it but for some reason its wrong. an someone please help me get these answers for (b).] An equation is given. (Enter your answers as …

More Similar Questions