It seems to me that integrating a polar equation should give you the(adsbygoogle = window.adsbygoogle || []).push({}); arc lengthof the curve, rather than the area under it. This is my reasoning:

A polar equation is in the form of:

(1) [tex]

r = f(\theta)

[/tex]

The arc length of a segment of a circle where the radius is constant is given by [tex]s = r\theta

[/tex]

If you let [tex] \theta -> 0[/tex] then r essentially becomes constant over the interval [θ , θ +dθ]

So, multiplying eq. (1) by [tex]d\theta[/tex] gives [tex]rd\theta = f(\theta)d\theta[/tex] and gives an arc length of zero width.

Now integrate with respect to [tex] \theta [/tex]:

[tex] \int{f(\theta)d\theta} = s[/tex] and you have the length of the curve.

Is my reasoning correct?

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# Integrating a polar equation

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