The area of the region, enclosed by the circle x^2+y^2=2, which is not common to the regio…

Question

The area of the region, enclosed by the circle $x^2+y^2=2$, which is not common to the region bounded by the parabola $y^2=x$ and the straight line $y=x$, is:

Accepted Answer

Required area = Area of circle -- $$\int\limits_0^1 {\left( {\sqrt x  - x} \right)dx} $$

= $$\pi $$r2 - $$\left( {{{2{x^{3/2}}} \over 3} - {{{x^2}} \over 2}} \right)_0^1$$

= $$\pi {\left( {\sqrt 2 } \right)^2}$$ - $${1 \over 6}$$

= $${1 \over 6}\left( {12\pi  - 1} \right)$$

Solutions · 1