Verified Solution • 2025–26 Session moderate

QJEEM19Mac102: JEE Main 2019 Mathematics - Class 12 JEEM19Mac102 Solution: Let     If I is minimum then the ordered pair…

Let   I=∫ab(x4−2x2)dx.{\rm I} = \int\limits_a^b {\left( {{x^4} - 2{x^2}} \right)} dx.   If I is minimum then the ordered pair (a, b) is -

Multiple Choice Options

  • A (2,−2)\left( {\sqrt 2 , - \sqrt 2 } \right)
  • B (0,2)\left( {0,\sqrt 2 } \right)
  • C (−2,2)\left( { - \sqrt 2 ,\sqrt 2 } \right)
  • D (−2,0)\left( { - \sqrt 2 ,0} \right)

Step-by-Step Verified Solution

Let f(x) = x2(x2 −- 2)

JEE Main 2019 (Online) 10th January Morning Slot Mathematics - Definite Integration Question 238 English Explanation
As long as f(x) lie below the x-axis, define integral will remain negative,
so correct value of (a, b) is ( −- 2\sqrt 2 , 2\sqrt 2 ) for minimum of I

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