AP EAMCET20227 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual
If f(x)= ( ⁻¹ x ) , then ₀^1 x f^ (x) d x=
Options
- A1- 3 2 2
- B- 1 2 2
- C1 2
- D- 2
Correct answer
B. - 1 2 2
Step-by-step solution
aligned f(x) & = ( ⁻¹ x ) f^ (x) & = ( ⁻¹ x ) x^2+1 I & = ₀^1 x f^ (x) d x= ₀^1 [x f^ (x) ]- ₀^1 f^ (x) d x & =f^ (1)- ₀^1[f(x)]= 1 2 2 - 1 2 & =- 1 2 2 aligned