MHT CET202415 May 2024Evening ShiftMathematicsIndefinite IntegrationActual
If f (x)= x x+1 , x -1 and (fof) (x)= F (x) , then F (x) d x is
Options
- Ax 2 + 1 2 (2 x+1)+ c , where c is a constant of integration.
- Bx 2 - 1 4 (2 x+1)+ c , where c is a constant of integration.
- Cx 2 - 1 2 (2 x+1)+ c , where c is a constant of integration.
- Dx 2 + 1 4 (2 x+1)+ c , where c is a constant of integration.
Correct answer
B. x 2 - 1 4 (2 x+1)+ c , where c is a constant of integration.
Step-by-step solution
aligned F (x) & =( fof )(x) & = f ( f (x)) & = f ( x x+1 ) & = x x+1 x x+1 +1 & = x 2 x+1 aligned aligned F (x) d x & = x 2 x+1 ~d x & = 1 2 (2 x+1)- 2 4 2 x+1 ~d x & = 1 2 ~d x- 1 4 2 2 x+1 ~d x & = 1 2 x- 1 4 |2 x+1|+c aligned