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- Thread starter freshman2013
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arildno

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No, you won't.

Do as your professor does.

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mathman

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CAF123

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There was a thread the other day where we wanted to find the length of the curve r=9+9cosθ.can you give me an example?

Following through the standard recipe of finding this, we arrive at the integral $$c \int_0^{2\pi} \sqrt{\cos^2\left(\frac{\theta}{2}\right)}\,d\theta,$$ where ##c## is a constant.

Doing as you say, writing ##\sqrt{\cos^2\left(\frac{\theta}{2}\right)} = \cos\left(\frac{\theta}{2}\right)## will give a zero length, which is clearly false.

The right way is of course ##\sqrt{\cos^2\left(\frac{\theta}{2}\right)} = |\cos\left(\frac{\theta}{2}\right)|## and this can be integrated by considering the sign of cos(θ/2) over the domain [0,2π].

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