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Question Number 66517 by mhmd last updated on 16/Aug/19

$$findtheareacos\left(2\theta \right)$$

Commented by MJS last updated on 16/Aug/19

$$\mathrm{you}\mathrm{must}\mathrm{give}\mathrm{borders}...$$

Answered by Smail last updated on 18/Aug/19

$$S=8{\int }_0^{\pi /4}\frac{1}{2}\left(r^{2}d\theta \right)=4{\int }_0^{\pi /4}{cos}^2\left(2\theta \right)d\theta$$$$=2{\int }_0^{\pi /4}(1+cos\left(4\theta \right))d\theta$$$$=2{[\theta +\frac{sin\left(4\theta \right)}{4}]}_0^{\pi /4}=\frac{\pi }{2}$$

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