Verified Solution • 2025–26 Session moderate

QJEEM16Maa23a: JEE Main 2016 Mathematics - Class 11 JEEM16Maa23a Solution: The area (in sq. units) of the region is :

The area (in sq. units) of the region {(x,y):y2≥2x   and   x2+y2≤4x,x≥0,y≥0}\left\{ {\left( {x,y} \right):{y^2} \ge 2x\,\,\,and\,\,\,{x^2} + {y^2} \le 4x,x \ge 0,y \ge 0} \right\} is :

Multiple Choice Options

  • A π−423\pi - {{4\sqrt 2 } \over 3}
  • B π2−223{\pi \over 2} - {{2\sqrt 2 } \over 3}
  • C π−43\pi - {4 \over 3}
  • D π−83\pi - {8 \over 3}

Step-by-Step Verified Solution

JEE Main 2016 (Offline) Mathematics - Area Under The Curves Question 131 English Explanation

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

Area == Area (OAB)−(OAB)- area under parabola ( 00 to 22 )

=π×(2)24−∫022x dx= {{\pi \times {{\left( 2 \right)}^2}} \over 4} - \int\limits_0^2 {\sqrt 2 \sqrt x } \,dx

=π−83= \pi - {8 \over 3}

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