Question

Find the average value of the function f(x) = x3 + 4 on the interval [2,4].

Answer 1

$f(x)=x^3+4$

Interval [2,4]

Average value of the function

$f_{avg}=\frac{1}{b-a}\int_{a}^{b}f(x)dx$

$=\frac{1}{4-2}\int_{2}^{4}(x^3+4)dx$

$=\frac{1}{2}\int_{2}^{4}(x^3+4)dx$

1 1. 3+1 23+1 + 4.c)

$=\frac{1}{2}[\frac{x^4}{4}+4x]_{2}^{4}$

$=\frac{1}{2}[\frac{(4)^4}{4}+4(4)-(\frac{(2)^4}{4}+4(2))]$

$=\frac{1}{2}[68]$

$\boldsymbol{=34}$