Finding the average value

Question

Find the average value of 𝑓(𝑥)=𝑥3�(�)=�3 on the interval [3,6][3,6].

Answer 1

The average value of f(x) = x³ on the interval [3,6] is [1 / (6-3)] ∫_{(from 3 to 6)} x³dx

= (1/12)x⁴_{(from 3 to 6)} = (1/12)(6⁴ - 3⁴)