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Integrals · Question 27

JEE Main 2026 (Online) 22nd January Morning ShiftMCQMedium📈 Topic in 71% papers+4−1
1

The value of - 2 2 ( 1[x] + 4 ) dx, where [ ] denotes the greatest integer function, is

  1. 160(21 - 1)
  2. 160( - 7)
  3. 760( - 3)
  4. 760(3 - 1)

Answer

(4) 760(3 - 1)

Solution

2 1.57, split at x = -1, 0, 1:

I = - /2-1 dx-2 + 4 + -10 dx-1 + 4 + 01 dx0 + 4 + 1 /2 dx1 + 4

= 12 ( 2 - 1 ) + 13 + 14 + 15 ( 2 - 1 )

= 710 ( 2 - 1 ) + 712

= 7 20 - 710 + 712

= 21 60 - 760 = 760(3 - 1)

Answer: (4)

JEE Main 2026 (Online) 22nd January Morning Shift

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2

If ( x) -112( x) -52 dx = - p1q1( x) 92 - p2q2( x) 52 - p3q3( x) 12 + p4q4( x) -32 + C, where pi and qi are positive integers with (pi, qi) = 1 for i = 1, 2, 3, 4 and C is the constant of integration, then 15p1p2p3p4q1q2q3q4 is equal to

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3

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4

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  2. 4
  3. 2
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7

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8

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  1. 2 + 3
  2. 4 +
  3. 1 + 3
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9

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  1. 12
  2. 9
  3. 6
  4. 4
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10

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  1. 3( +1)
  2. 3 3( +6)
  3. 3( +2)
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