The value of _ -3 ^3 ^7 x ¹⁶ x ~d x is

Step-by-step solution

The integral I = _ -3 ^3 ^7 x ¹⁶ x d x is evaluated by examining the parity of the integrand. For f(x) = ^7 x ¹⁶ x , we compute f(-x) = ^7 (-x) ¹⁶ (-x) = (- x)^7 ( x)¹⁶ = - ^7 x ¹⁶ x = -f(x) , confirming that f is an odd function. Since f is odd and the interval [-3, 3] is symmetric about zero, the definite integral evaluates to zero. I = _ -3 ^3 ^7 x ¹⁶ x d x = 0