Question

The area bounded by the curves $y^2\le 9x$ , $(x-2{)}^2+y^2\ge 4$ and $y\ge (x-4)$ in the first quadrant is

• A. $(56-2\pi )\text{sq.units}$
• B. $(56+2\pi )\text{sq.units}$
• C. $(64+2\pi )\text{sq.units}$
• D. $(64-2\pi )\text{sq.units}$

Answer 1

The correct option is A $(56-2\pi )\text{sq.units}$



Area $={\int }_0^{16}\sqrt{9x}-{\int }_4^{16}(x-4)dx-$ Area of the semicircle
$\Rightarrow \text{Area}=128-\left[\right(128-64)-(-8\left)\right]-2\pi =(56-2\pi )\text{sq.units}$