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Integrals

JEE Main 2026 (Online) 5th April Evening ShiftMCQMedium📈 Topic in 24% papers+4−1
Ques. 1JEE Main 2026, 5 April (Evening Shift)

Let (21-a+21+a ), f(a), (3a+3-a ) be in A.P. and be the minimum value of f(a). Then the value of the integral e( -1) e( ) dx (e2x-e-2x ) is :

  1. 12 e ( 43 )
  2. 14 e ( 43 )
  3. 12 e ( 85 )
  4. 14 e ( 85 )

Answer

(2) 14 e ( 43 )

Solution

Since the three terms are in A.P.,

2f(a) = (21 - a + 21 + a ) + (3a + 3-a ) = 2 (2a + 2-a ) + (3a + 3-a )

By A.M. G.M., 2a + 2-a 2 and 3a + 3-a 2 (equality at a = 0), so

2f(a) 6 f(a) 3 = 3

I = e2 e3 dxe2x - e-2x = e2 e3 e2x dxe4x - 1

Put e2x = u, so 2e2xdx = du and the limits become u = 4 to u = 9:

I = 12 49 duu2 - 1 = 14 [ e u - 1u + 1 ]49

I = 14 [ e 810 - e 35 ] = 14 e ( 45 53 )

I = 14 e ( 43 )

Answer: (2)

Keep practising — Integrals

Ques. 2JEE Main 2026, 5 April (Evening Shift)

Let f : [1, ) R be a differentiable function defined as f(x)= 1x f(t) dt +(1-x) ( e x-1 )+e. Then the value of f(f(1)) is :

  1. (1+ee )
  2. (1+e)
  3. (1+e+ee )
  4. 1+2e
Ques. 3JEE Main 2026, 4 April (Morning Shift)

Let -22 (| x|+[x x] )dx=2(3- 2)+ , where [ ] is the greatest integer function. Then ( 2 ) equals:

  1. 1
  2. 2
  3. 4
  4. 8
Ques. 4JEE Main 2026, 4 April (Evening Shift)

If =1 and =1+i 2, where i= -1 are two roots of the equation x3+ax2+bx+c=0, a, b, c R, then -11 (x3+ax2+bx+c )dx is equal to :

  1. -2
  2. -4
  3. -8
  4. -10
Ques. 5JEE Main 2026, 4 April (Evening Shift)

The integral 01 -1 (1+x+x2 )dx is equal to :

  1. 2 -12+ 12 e ( 54 )+ 2
  2. 2 -12+ 12 e ( 54 )- 2
  3. 2 -12- 12 e ( 54 )+ 2
  4. 2 -12- 12 e ( 54 )- 2
Ques. 6JEE Main 2026, 2 April (Morning Shift)

Let [.] denote the greatest integer function. Then the value of 03 ( ex+e-x[x]! )dx is :

  1. e2+e3- 1e2- 1e3
  2. 12 (e2+e3- 1e2- 1e3 )
  3. e2+e3- 12e2- 12e3
  4. 12 (e2+e3 )- 1e2- 1e3
Ques. 7JEE Main 2026, 2 April (Morning Shift)

If = 02 3 2 (x2+4 )dx+ 24 2x-4 dx, then 2 is equal to .

Ques. 8JEE Main 2026, 2 April (Evening Shift)

The value of 020 ( 4 x+ 4 x )dx is equal to:

  1. 15 2
  2. 25
  3. 15
  4. 25 2
Ques. 9JEE Main 2026, 2 April (Evening Shift)

Let f(x)= ( 16x+24x2+2x-15 )dx. If f(4)=14 e(3) and f(7)= e (2 3 ), , N, then + is equal to :

  1. 31
  2. 37
  3. 39
  4. 41
Ques. 10JEE Main 2026, 28 January (Morning Shift)

Let f be a polynomial function such that f(x2 + 1) = x4 + 5x2 + 2, for all x R. Then 03 f(x) dx is equal to

  1. 332
  2. 53
  3. 272
  4. 413
Ques. 11JEE Main 2026, 28 January (Morning Shift)

If ( 1 - 5 2 x 5 x 2 x )dx = f(x) + C, where C is the constant of integration, then f ( 6 ) - f ( 4 ) is equal to

  1. 1 3(26 - 3)
  2. 4 3(8 - 6)
  3. 1 3(26 + 3)
  4. 2 3(4 + 6)

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