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MHT CET20243 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

If f ( x-4 x-2 )=2 x+1, x R - 1,-2 , then f (x) d x is equal to

Options

  1. A5 x-4 (x-1)+ c , where c is constant of integration.
  2. Bx-4 (x-1)+c , where c is constant of integration.
  3. C5 x+4 (x-1)+ c , where c is constant of integration.
  4. D5 x+ (x-1)+ c , where c is constant of integration.

Correct answer

A. 5 x-4 (x-1)+ c , where c is constant of integration.

Step-by-step solution

aligned & f ( x-4 x-2 )=2 x+1 & Let x-4 x-2 =y & x-2-2 x-2 =y & 1- 2 x-2 =y & -2 x-2 =y-1 & -2 y-1 =x-2 & x= -2 y-1 +2 & 2 x= -4 y-1 +4 & 2 x+1= -4 y-1 +5 aligned aligned & f (y)= -4 y-1 +5 & f (x)= -4 x-1 +5 & f (x) d x= -4 x-1 +5 & =-4 (x-1)+5 x+c & =5 x-4 (x-1)+c aligned

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