_ /6 ^ /3 x - x 1 + x x ,dx =

Step-by-step solution

Let I = _ /6 ^ /3 x - x 1 + x x ,dx Using the definite integral property _ a ^ b f(x) ,dx = _ a ^ b f(a+b-x) ,dx , we substitute x with 6 + 3 - x = 2 - x . I = _ /6 ^ /3 ( 2 - x) - ( 2 - x) 1 + ( 2 - x) ( 2 - x) ,dx I = _ /6 ^ /3 x - x 1 + x x ,dx I = - _ /6 ^ /3 x - x 1 + x x ,dx I = -I 2I = 0 I = 0 Answer: 0