Verified Solution • 2025–26 Session moderate

QJEEM20Ma4ed9: JEE Main 2020 Mathematics - Class 12 JEEM20Ma4ed9 Solution: The area of the region, enclosed by the circle x 2 + y 2 = 2…

The area of the region, enclosed by the circle x2 + y2 = 2 which is not common to the region bounded by the parabola y2 = x and the straight line y = x, is:

Multiple Choice Options

  • A 16(24π−1){1 \over 6}\left( {24\pi - 1} \right)
  • B 13(12π−1){1 \over 3}\left( {12\pi - 1} \right)
  • C 13(6π−1){1 \over 3}\left( {6\pi - 1} \right)
  • D 16(12π−1){1 \over 6}\left( {12\pi - 1} \right)

Step-by-Step Verified Solution

JEE Main 2020 (Online) 7th January Morning Slot Mathematics - Area Under The Curves Question 108 English Explanation

Required area = Area of circle – ∫01(x−x)dx\int\limits_0^1 {\left( {\sqrt x - x} \right)dx}

= π\pi r2 - (2x3/23−x22)01\left( {{{2{x^{3/2}}} \over 3} - {{{x^2}} \over 2}} \right)_0^1

= π(2)2\pi {\left( {\sqrt 2 } \right)^2} - 16{1 \over 6}

= 16(12π−1){1 \over 6}\left( {12\pi - 1} \right)

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