Show that the given functions are orthogonal on the indicated interval. f1(x) = x, f2(x) = x4; [−2, 2]

Question

Give integrand in terms of x 

Answer 1

Dot-product f₁(x)•f₂(x) = ∫_-2²x·x⁴dx = ∫_-2²x⁵dx = 0 becouse integral of odd function in symmetric likmits.

Because functions f₁ and f₂ are orthogonal on interval [-2,2]