Solution:
Given equations are
The area bounded by the circle and parabola
![=2[\text { Area }(\mathrm{OADO})+\text { Area }(\mathrm{ADBA})]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3d19ee48f55ee60eaa643e317a571a54_l3.png "Rendered by QuickLaTeX.com")
![(\mathrm{ADBA})]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ef1a2ae959cf9f01933c7ebf78eb8d5c_l3.png "Rendered by QuickLaTeX.com")
![=2\left[\int_{0}^{2} \sqrt{16 x} d x+\int_{2}^{4} \sqrt{16-x^{2}} d x\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-749a875f398a7ab9b25ad0ced4813f9d_l3.png "Rendered by QuickLaTeX.com")
![=2\left[\sqrt{6}\left\{\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right\}_{0}^{2}\right]+2\left[\frac{x}{2} \sqrt{16-x^{2}}+\frac{16}{2} \sin ^{-1} \frac{x}{4}\right]_{2}^{4}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-77c4c747487bf6bb3d0ecbaf5ee9239a_l3.png "Rendered by QuickLaTeX.com")
![=2 \sqrt{6} \times \frac{2}{3}\left[x^{\frac{3}{2}}\right]_{0}^{2}+2\left[8 \cdot \frac{\pi}{2}-\sqrt{16-4}-8 \sin ^{-1}\left(\frac{1}{2}\right)\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c21c916b761de2523aa70976e9f46c6b_l3.png "Rendered by QuickLaTeX.com")
![=\frac{4 \sqrt{6}}{3}(2 \sqrt{2})+2\left[4 \pi-\sqrt{12}-8 \frac{\pi}{6}\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4d2888c69e1da041448702d8c9bd1071_l3.png "Rendered by QuickLaTeX.com")
![=\frac{4}{3}[4 \sqrt{3}+6 \pi-3 \sqrt{3}-2 \pi]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f40c3b6d2e0d87b5e269689acb4e465b_l3.png "Rendered by QuickLaTeX.com")
![=\frac{4}{3}[\sqrt{3}+4 \pi]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-336cef8adff07c1074704946c8646f64_l3.png "Rendered by QuickLaTeX.com")
![=\frac{4}{3}[4 \pi+\sqrt{3}]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-50cc04102a4b908af381cdfb56ea7b1e_l3.png "Rendered by QuickLaTeX.com")
Area of circle 
![=16 \pi-\frac{4}{3}[4 \pi+\sqrt{3}]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-56e4b6f65816a018b9c6f37d1804378d_l3.png "Rendered by QuickLaTeX.com")
![=\frac{4}{3}[4 \times 3 \pi-4 \pi-\sqrt{3}]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-92c47f9fd29caee3d28eb2687e264e1c_l3.png "Rendered by QuickLaTeX.com")
As a result, the correct answer is 
Choose the correct option: The area of the circle 
A. 
B. 
C. 
