Let (f(x)= ⁻¹ ( 1+ x x ) ); (g(x)= ⁻¹ ( x 1- x ) ), then ( (f(x)+g(x)) d x= )

Step-by-step solution

( aligned f(x) & = ⁻¹ ( 1+ x x ) & = ⁻¹ ( 2 ^2 x 2 2 x 2 x 2 )= ⁻¹ ( x 2 ) & = ⁻¹ [ ( 2 - x 2 ) ]= 2 - x 2 and g(x) & = ⁻¹ ( x 1- x ) & = ⁻¹ ( 2 x / 2 x / 2 2 x / 2 )= ⁻¹ ( x 2 ) & = ⁻¹ [ ( 2 - x 2 ) ]= 2 - x 2 (f(x) & +g(x)) d x= ( -x) d x= x- x^2 2 +c aligned ) Hence, option (b) is correct.