`y=ln(sinx) , [pi/4 , (3pi)/4]` Find the arc length of the graph of the function over the indicated interval.

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The arc length of a function of x, f(x), over an interval is determined by the formula below:

`L=int_a^bsqrt(1+((dy)/(dx))^2)dx`

So using the function given, let us first find `(dy)/(dx):`

`d/(dx)(ln(sin(x)))=(1/(sin(x)))*(cos(x))=(cos(x))/(sin(x))=cot(x)`

We can now substitute this into our formula above:

`L=int_a^bsqrt(1+((dy)/(dx))^2)dx=int_(pi/4)^((3pi)/4)sqrt(1+(cot(x))^2)dx`

Which can then be simplified to:

(The entire section contains 253 words.)

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