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JEE Main20249 Apr 2024Morning ShiftMathematicsIndefinite IntegrationActual

Let 2- x 3+ x ~d x= 1 2 ( x+ _ e | x+ x| )+C , where C is the constant of integration. Then + is equal to :

Options

  1. A7
  2. B4
  3. C1
  4. D3

Correct answer

B. 4

Step-by-step solution

aligned & 2- x 3+ x d x= 2 x- x 3 x+ x d x & 2 x- x=A(3 x+ x)+B( x-3 x) & 3 A+B=2 & A-3 B=-1 aligned aligned & A= 1 2 , B= 1 2 & 2 x- x 3 x+ x d x & = x 2 + 1 2 |3 x+ x|+C & = 1 2 (x+ |3 x+ x|)+C & = 1 2 ( x+ | x+ x|)+C & =1, =1, =3 & + =1+ 3 1 =4 aligned

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