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Integrals

JEE Main 2025 (Online) 23rd January Evening ShiftMCQMedium📈 Topic in 21% papers+4−1
Ques. 1JEE 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

Answer

(2) 55

Solution

Repeated integration by parts (DI method): g(x)=-x3 x+3x2 x+6x x-6 x

At 2: g= 3 24-6 and g'=x3 x= 38

8(g+g')= 3+6 2-48 =1, =6, =-48

+ - =55

Answer: (2)

Keep practising — Integrals

Ques. 2JEE 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
  4. 2
Ques. 3JEE 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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