Question

Find the average value of the function g on the given interval, [1.2].

g(x) = 5x^2(8+x^3)^(1/2).

I attached a picture of the equation. Thank you so much, guys!

Answer 1

\[\overline{g(x)}={\int_a^bg(x)dx\over b-a}\]

Answer 2

where \(\overline{g(x)}\) is the average value of g(x)

Answer 3

\[g _{ave}=\frac{\int\limits_{a}^{b} gdx}{b-a}\]

Answer 4

\[we \ \ have \ \ g(x)=5x^2\sqrt{8+x^3} \ \ \ a=1 , b=2\]

Answer 5

\[g _{ave}=\int\limits_{1}^{2} 5x^2\sqrt{8+x^3} dx= \frac{10}{9} (8+x^3)^{3/2} \ from \ 1 \ \to \ 2=\frac{370}{9}\]

Answer 6

Thank you so much, mukushla!