what is the average value of f(x) = |x3| over [-2,1]

Question

x³

not x3

Answer 1

Use the MVT for integrals formula: Avg value of f on [a,b] = ∫_a^b f(x)dx / (b-a)

(Btw, what we are doing here is finding the height of a rectangle of width (b-a) that has the same area as the area under the curve, f(x). This height is f(x)'s average y-value on that closed interval):

1/4⋅x⁴]_-2¹ ÷ 3 = - 1.25