Mathematics - Area Under Curves Question with Solution | TestHub

$\begin{array}{rl}\text{ Required area }& =2{\int }_0^7\sqrt{49-x^2}\mathrm{d}x\\ & =2{\left[\frac{x}{2}\sqrt{49-x^2}+\frac{49}{2}{\sin }^{-1}\left(\frac{x}{7}\right)\right]}_0^7\\ & =2\left[\frac{7}{2}\sqrt{49-49}+\frac{49}{2}{\sin }^{-1}\left(\frac{7}{7}\right)\right]-0\\ & =2\times \frac{49}{2}\times \frac{\pi }{2}\\ & =\frac{49\pi }{2}\text{ sq. units }\end{array}$