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## Homework Statement

Hey all, I'm trying to calculate the length of the cardioid r(θ)=1+cosθ (polar coordinates) and I figured I'd try to do it in one integral from 0 to 2Pi.

## Homework Equations

So the integral is [tex]\int_{0}^{2\pi} \sqrt{r^2 + (\frac{dr}{d\theta})^2}d\theta[/tex]

## The Attempt at a Solution

and it becomes [tex]\int_{0}^{2\pi} \sqrt{1+cos\theta} d\theta[/tex] which becomes I've found

[tex]\int_{0}^{2\pi} \sqrt{1+cos\theta} d\theta = \int_{0}^{2\pi} \frac{sin\theta}{\sqrt{1-cos\theta}} d\theta = 2\sqrt{1-cos\theta} |_{0}^{2\pi}[/tex]

but that gives me 0 , although I run it through mathematica and it gives me [tex]4sqrt{2}[/tex]. Why?

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