The area (in sq.

Question

The area (in sq. units) of the region $\{(x,y) : y^2\ge2x$ and $x^2+y^2\le4x,\ x\ge0,\ y\ge0\}$ is:

Accepted Answer

Points of intersection of the two curves are $$\left( {0,0} \right),\left( {2,2} \right)$$ and $$\left( {2, - 2} \right)$$

Area $=$ Area $(OAB)-$ area under parabola ($0$ to $2$ )

$$ = {{\pi  \times {{\left( 2 \right)}^2}} \over 4} - \int\limits_0^2 {\sqrt 2 \sqrt x } \,dx$$

$$ = \pi  - {8 \over 3}$$

Solutions · 1