MHT CET20225 Aug 2022Evening ShiftMathematicsIndefinite IntegrationActual
If f ( x )= x ^2+ ^2 x 1+ x ^2 , ^2 x d x and f (0)=0 , then f (1)=
Options
- A4 -1
- B1+ 4
- C1- 4
- D1- 4
Correct answer
D. 1- 4
Step-by-step solution
aligned & f ( x )= x ^2+ ^2 x 1+ x ^2 ^2 x d x & = 1+ x ^2+ ^2 x -1 1+ x ^2 ^2 x d x & = (1- ^2 x 1+ x ^2 ) ^2 x d x & = ^2 x d x - dx 1+ x ^2 & = f ( x )= x - ⁻¹ x + C & f (0)=0 c =0 aligned So, f ( x )= x - ⁻¹ X f (1)= 1- ⁻¹(1)= (1)- 4