The area (in sq. units) of the region\left \{ \left ( x,y \right ):y^{2}\geqslant 2x \: and\: x^{2}+y^{2}\leq 4x,x\geqslant 0,y\geqslant 0\right \}is

  • Option 1)

    \pi -\frac{4}{3}

  • Option 2)

    \pi -\frac{8}{3}

  • Option 3)

    \pi -\frac{4\sqrt{2}}{3}

  • Option 4)

    \frac{\pi }{2} -\frac{2\sqrt{2}}{3}

 

Answers (1)

 

Area along x axis -

Let y_{1}= f_{1}(x)\, and \, y_{2}= f_{2}(x) be two curve then area bounded between the curves and the lines

x = a and x = b is

\left | \int_{a}^{b} \Delta y\, dx\right |= \left | \int_{a}^{b}\left ( y_{2}-y_{1} \right ) dx\right |

 

- wherein