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Question Number 207169 by hardmath last updated on 08/May/24

$$\mathrm{Find}:{\int }_0^3\sqrt{9-{\mathrm{x}}^2}\mathrm{dx}=?$$

Answered by lepuissantcedricjunior last updated on 08/May/24

$${\int }_0^3\sqrt{9-{\mathbf{x}}^2}\mathbf{dx}=\frac{\mathit{\pi }{3}^2}{4}=\frac{9}{4}\mathit{\pi }$$$$\mathit{c}\mathit{a}\mathit{r}\mathrm{\forall }\mathit{a}\in {\mathbb{R}}_{+}^{\ast }{\int }_0^{\mathit{a}}\sqrt{{\mathit{a}}^2-{\mathit{x}}^2}\mathit{d}\mathit{x}=\frac{{\mathit{a}}^2}{4}\mathit{\pi }$$$$...........$$

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