NDA2019MathematicsIndefinite IntegrationActual
What is d x 2 x^2-2 x+1 equal to?
Options
- A⁻¹(2 x-1) 2 +c
- B2 ⁻¹(2 x-1)+c
- C⁻¹(2 x+1) 2 +c
- D⁻¹(2 x-1)+c
Correct answer
D. ⁻¹(2 x-1)+c
Step-by-step solution
aligned & d x 2 x^2-2 x+1 = 1 2 d x x^2-x+ 1 2 & = 1 2 d x (x- 1 2 )^2+ ( 1 2 )^2 & = 1 2 [ 1 1 2 ⁻¹ ( x- 1 2 1 2 ) ]+C & = 1 2 2: ⁻¹(2 x-1)+C & = ⁻¹(2 x-1)+C aligned