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!

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!

anonymous · Answer

attachment

turingtest · Answer

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

turingtest · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Thank you so much, mukushla!