MHT CET20244 May 2024Evening ShiftMathematicsIndefinite IntegrationActual
⁻¹ ( 1- x 1+ x ) d x=
Options
- A4 x-x+c , where c is a constant of integration.
- B4 - x 2 + c , where c is a constant of integration.
- C4 x- x^2 4 + c , where c is a constant of integration.
- D4 x+ x^2 4 + c , where c is a constant of integration.
Correct answer
C. 4 x- x^2 4 + c , where c is a constant of integration.
Step-by-step solution
Let I = ⁻¹ ( 1- x 1+ x ) d x= ⁻¹ ( ^2 x 2 + ^2 x 2 -2 x 2 x 2 ^2 x 2 + ^2 x 2 +2 x 2 x 2 ) d x= ⁻¹ ( ( x 2 - x 2 )^2 ( x 2 + x 2 )^2 ) d x aligned & = ⁻¹ ( x 2 - x 2 x 2 + x 2 ) d x & = ⁻¹ ( 1- x 2 1+ x 2 ) d x aligned aligned & = ⁻¹ ( ( 4 - x 2 ) ) d x & = ( 4 - x 2 ) d x & = 4 x- x^2 4 + c aligned