JEE Main202523 Jan 2025Evening ShiftMathematicsIndefinite IntegrationActual

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

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Correct answer

B. 55

Step-by-step solution

aligned & x^3 x d x=-x^3 x+ 3 x^2 x d x & =-x^3 x+3 x^2 x- 6 x x d x & =-x^3 x+3 x^2 x+6 x x-6 x+c aligned So g(x)=-x^3 x+3 x^2 x+6 x x-6 x aligned & g ( 2 )= 3 ^2 4 -6 & ~g ^ ( x )=-3 x ^2 x + x ^3 x +6 x -6 x & ~g ^ ( 2 )= ^3 8 & 8 ( ~g ( 2 )+ g ^ ( 2 ) )= ^3+6 ^2-48 aligned So + - =55

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