Hi, I've been having some issues in solving this problem.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Find the arc length of r=2/(1-cosθ) from π/2 to π

2. Relevant equations

L =(integrate) sqrt(r^{2}+(dr/dθ)^{2})dθ

3. The attempt at a solution

I found (dr/dθ) = (-2sinθ)/(1-cosθ)^{2}

so (dr/dθ)^{2}= (4sin^{2}θ)/(1-cosθ)^{4}

Then r^{2}= 4/(1-cosθ)^{2}

both have a factor of 4/(1-cosθ)^{2}, so I pulled that outside the sqrt to get

L=(integrate) 2/(1-cosθ) * sqrt(1+(sin^{2}θ)/(1-cosθ)^{2})

then I multiplied the 1 by (1-cosθ)^{2}/(1-cosθ)^{2}to give common denominators.

After multiplying it out, the numerator of the fraction was 1-2cosθ+cos^{2}θ+sin^{2}θ, so I got rid of the sin and cos and added a 1 to get 2 - 2cosθ

I pulled out a factor of sqrt2 and ended up with:

L = (integrate) 2sqrt2/(1-cosθ) * sqrt(1/(1-cosθ))

or

L= (integrate) 2sqrt2*(1-cosθ)^{-3/2}

This is where I got stuck. I can't think of any way to integrate that problem using any of the means we have gone over so far.

Some direction in which way to go would be extremely helpful, thanks in advance.

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# Homework Help: Finding the Arc Length of a Polar Function

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