AP EAMCET202316 May 2023Morning ShiftMathematicsDefinite IntegrationActual
3. ₀^ 1 2 x ⁻¹ x 1-x^2 d x=
Options
- A( 1 2 + 3 12 )
- B( 1 2 - 3 12 )
- C(- 1 2 + 3 12 )
- D(- 1 2 - 3 12 )
Correct answer
B. ( 1 2 - 3 12 )
Step-by-step solution
₀^ 1 / 2 x ⁻¹ x 1-x^2 d x= ₀^ 1 / 2 x ⁻¹ x 1 1-x^2 d x ...(i) Let ⁻¹ x=t t=x Substituting above values in eqn. (i), we get : ₀^ 1 / 2 x ⁻¹ x 1-x^2 d x= ₀^ / 6 t t d t aligned & =[t(- t)+ t]₀^ / 6 & = [- 6 ( 6 )+ ( 6 )-0-0 ] & = [- 6 3 2 + 1 2 ]= 1 2 - 3 12 aligned