AP EAMCET20228 Jul 2022Morning ShiftMathematicsIndefinite IntegrationActual
⁻¹ (1-x+x^2 ) d x+ ⁻¹(x) d x+ ⁻¹(1-x) d x=
Options
- A2 x+C
- B4 x+C
- Cx+C
- Dx+C
Correct answer
A. 2 x+C
Step-by-step solution
I= ⁻¹ (1-x+x^2 ) d x+ ⁻¹ x d x+ ⁻¹(1-x) d x aligned & = [ ⁻¹ (1-x+x^2 ) d x+ ⁻¹ ( x+1-x 1-x(1-x) ) ] d x & = [ ⁻¹ (1-x+x^2 )+ ⁻¹ ( 1 1-x+x^2 ) ] dx & = [ ⁻¹ (1-x+x^2 ) d x+ ⁻¹ (1-x+x^2 ) ] d x & = 2 d x= 2 x+C aligned