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QJEEM21Ma3ac0: JEE Main 2021 Mathematics - Class 12 JEEM21Ma3ac0 Solution: The area of the region : is :

The area of the region : R={(x,y):5x2≤y≤2x2+9}R = \{ (x,y):5{x^2} \le y \le 2{x^2} + 9\} is :

Multiple Choice Options

  • A 636\sqrt 3 square units
  • B 12312\sqrt 3 square units
  • C 11311\sqrt 3 square units
  • D 939\sqrt 3 square units

Step-by-Step Verified Solution

JEE Main 2021 (Online) 24th February Evening Shift Mathematics - Area Under The Curves Question 96 English Explanation
Required area

=2∫03(2x2+9−5x2)dx= 2\int\limits_0^{\sqrt 3 } {\left( {2{x^2} + 9 - 5{x^2}} \right)} dx

=2∫03(9−3x2)dx= 2\int\limits_0^{\sqrt 3 } {\left( {9 - 3{x^2}} \right)dx}

=2∣ 9x−x3 ∣03=123= 2|\,9x - {x^3}\,|_0^{\sqrt 3 } = 12\sqrt 3

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