AP EAMCET201824 Apr 2018Morning ShiftMathematicsIndefinite IntegrationActual
If g ( t+1 2 t+1 )=t+1 , then g(x) d x=
Options
- Ax^2 2 +c
- B_e(2 x-1)+ 1 2 _e|(x+1)|+c
- C1 2 _e | ( x+1 2 x+1 ) |+c
- Dx 2 + 1 4 _e|2 x-1|+c
Correct answer
D. x 2 + 1 4 _e|2 x-1|+c
Step-by-step solution
g ( t+1 2 t+1 )=t+1 replacing t+1 2 t+1 by x , we get, gathered t+1 2 t+1 =x t+1=2 t x+x t(1-2 x)=x-1 t= x-1 1-2 x g(x)= x-1 1-2 x +1= x-1+1-2 x 1-2 x g(x)= -x 1-2 x g(x) d x= -x 1-2 x d x = 1 2 1-2 x-1 1-2 x d x= 1 2 [ 1 d x- 1 1-2 x d x ] = 1 2 [x+ 1 2 |2 x-1| ]= x 2 + 1 4 _e|2 x-1|+C . gathered