Imagine a curve such as $$r=\sqrt{\sin x}$$

The area over $(0,\pi)$ would be calculated as follows:

$$\int_0^{\pi}\frac{1}{2}\sqrt{\sin x}^2dx=\int_0^{\pi}\frac{1}{2}|{\sin x}|dx, not \int_0^{\pi}\frac{1}{2}{\sin x}dx$$ correct?

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    $\begingroup$ Since $\sin x$ is nonnegative on $[0,\pi]$, you can remove the absolute value symbol. $\endgroup$ – John Thompson May 3 at 3:17
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    $\begingroup$ I just realized that as i posted the question! Crap, i feel really stupid. Thanks though. $\endgroup$ – Roshan May 3 at 3:18

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