₀^ / 2 x- x 1+ x x d x is equal to

Step-by-step solution

aligned & Let I= ₀^ / 2 x- x 1+ x x d x ...(i) & aligned & I= ₀^ / 2 ( 2 -x )- ( 2 -x ) 1+ ( 2 -x ) ( 2 -x ) d x & [ ₀^a f(x) d x= ₀^a f(a-x) d x ] aligned & = ₀^ / 2 x- x 1+ x x d x ...(ii) & [ ( 2 -x )= x and ( 2 -x )= x ] aligned On adding Eqs. (i) and (ii), we get 2 I= ₀^ / 2 0 1+ x x d x=0 I=0