Thursday

April 17, 2014

April 17, 2014

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

y = ln (sin(x))

,[π/4,3π/4]

- calculus -
**Steve**, Wednesday, January 25, 2012 at 1:15pmy = 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)

**Related Questions**

calculus - Find the arc length of the graph of y = x from x = 0 to x = 3 using ...

calculus - Find the length of the arc formed by y = (1/8)(4x^2-2ln(x)) from x=4 ...

calculus - Find the arc length of the graph of the function over the indicated ...

calculus - find the arc length from (x1,y2) to (x2,y2) on the graph F(x)=mx+b

Math rem - 2.Find the length of the arc in a circle if the radius of the circle ...

Calculus - A pendulum swings through an arc length of 1120 cm (Swing #1). With ...

Calculus Hard Question - A pendulum swings through an arc length of 1120 cm (...

Precalculus - Instead of graphing the arc length against the height, Olivia ...

calc arc length - Find the length of the arc along f(x) = integral from 0 to x^3...

maths - find the radius of the circle if length of arc is 4p cm and angle made ...