MHT CET20225 Aug 2022Morning ShiftMathematicsIndefinite IntegrationActual
1- x 1+ x d x= (where C is a constant of integration)
Options
- A-2 1-x - ⁻¹ x + x(1-x)
- B-2 1-x + ⁻¹ x + x(1-x)
- C2 1-x + ⁻¹ x + x(1-x)
- D-2 1-x + ⁻¹ x - x(1-x)
Correct answer
B. -2 1-x + ⁻¹ x + x(1-x)
Step-by-step solution
aligned & 1- x 1+ x d x= (1- x )^2 1-x d x & 1- x 1-x d x= d x 1-x - x 1-x d x & -2 1-x - ^2 1- ^2 (-2 d ) [ let x= ^2 ] & =-2 1-x + 2 ^2 d & aligned aligned & =-2 1-x + (1+ 2 ) d & =-2 1-x + + 2 2 +C & =-2 1-x + + +C & =-2 1-x + ⁻¹ x + 1-x x +C & =-2 1-x + ⁻¹ x + x(1-x) +C aligned