show that the integral of x^5 dx on [0,1] is smaller or equal to the integral of x^4 dx on [0,1]

Answer 1

On [0,1]

x ≤ 1; therefore x⁵ < x⁴ on that interval.

For this reason the integral on [0,1] of x⁵ is less than the integral of x⁴ on this interval.