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Integrals

JEE Main 2025 (Online) 23rd January Morning ShiftMCQMedium📈 Topic in 66% papers+4−1
Ques. 1JEE Main 2025, 23 January (Morning Shift)

The value of e2e4 1x ( e (( ex)2+1 )-1e (( ex)2+1 )-1+e ((6- ex)2+1 )-1 )dx is

  1. 1
  2. loge 2
  3. e2
  4. 2

Answer

(1) 1

Solution

Put t= x: I= 24 f(t)f(t)+f(6-t)dt, f(t)=e 1t2+1, and a+b=2+4=6

King property (t 6-t): I= 24 f(6-t)f(t)+f(6-t)dt

Add: 2I= 24dt=2 I=1

Answer: (1)

Keep practising — Integrals

Ques. 2JEE Main 2025, 23 January (Morning Shift)

Let I(x)= dx(x-11) 1113(x+15) 1513. If I(37)-I(24)= 14 ( 1b 113- 1c 113 ), b,c N, then 3(b+c) is equal to

  1. 39
  2. 22
  3. 40
  4. 26
Ques. 3JEE Main 2025, 23 January (Evening Shift)

If I= 0 2 32x 32x+ 32x dx, then 02I x x x 4x+ 4x dx equals :

  1. 212
  2. 24
  3. 216
  4. 28
Ques. 4JEE Main 2025, 23 January (Evening Shift)

Let x3 x dx=g(x)+C, where C is the constant of integration. If 8 (g ( 2 )+g' ( 2 ) )= 3+ 2+ , , , Z, then + - equals :

  1. 47
  2. 55
  3. 62
  4. 48
Ques. 5JEE Main 2025, 22 January (Morning Shift)

Let for f(x)=7 8x+7 6x-3 4x-3 2x, I1= 0 /4f(x) dx and I2= 0 /4x f(x) dx. Then 7I1+12I2 is equal to :

  1. 2
  2. 1
  3. 2
Ques. 6JEE Main 2025, 22 January (Evening Shift)

If x ( x -1x 1-x2+ -1x(1-x2)3/2+ x1-x2 )dx=g(x)+C, where C is the constant of integration, then g ( 12 ) equals :

  1. 6 e3
  2. 6 e2
  3. 4 e3
  4. 4 e2

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