BITSAT2009MathematicsDefinite IntegrationActual
Evaluate: ( x ⁻¹ x d x )
Options
- A( 1 2 (x^2+1 ) ⁻¹ x- 1 2 x+c )
- B( 1 2 (x^2+1 ) ⁻¹ x+ 1 2 x+c )
- C( 1 2 ( x ^2-1 ) ⁻¹ x - 1 2 x + c )
- DNone of these
Correct answer
A. ( 1 2 (x^2+1 ) ⁻¹ x- 1 2 x+c )
Step-by-step solution
( aligned & x ⁻¹ x d x= x^2 2 ⁻¹ x- 1 2 x^2 1+x^2 d x & = x^2 2 ⁻¹ x- 1 2 [1- 1 1+x^2 ] d x & = 1 2 (x^2+1 ) ⁻¹ x- 1 2 x+c aligned )