MHT CET202618 April 2026Morning ShiftMathematicsInverse Trigonometric FunctionsActual
If 0 x 1 , I₁ = ⁻¹ 1-x^2 ,dx and I₂ = ⁻¹x ,dx , then which of the following is true?
Options
- AI₁ = I₂
- BI₁ = 2 I₂
- CI₁ + I₂ = 2 x
- DI₁ + I₂ = 2
Correct answer
C. I₁ + I₂ = 2 x
Step-by-step solution
For 0 x 1 , the inverse trigonometric identity is: ⁻¹ 1-x^2 = ⁻¹x Substituting this into I₁ : I₁ = ⁻¹x ,dx Given: I₂ = ⁻¹x ,dx Adding I₁ and I₂ : I₁ + I₂ = ⁻¹x ,dx + ⁻¹x ,dx I₁ + I₂ = ( ⁻¹x + ⁻¹x) ,dx Using the identity ⁻¹x + ⁻¹x = 2 : I₁ + I₂ = 2 ,dx I₁ + I₂ = 2 x Answer: I₁ + I₂ = 2 x