## anonymous 5 years ago find the average value of y=(x^2)[sq root of (x^3+1)]

1. anonymous

2. nikvist

what is interval?

3. anonymous

[0,2]

4. nikvist

$\frac{1}{2}\int\limits_0^2x^2\sqrt{x^3+1}dx=\quad;\quad y=x^3+1,dy=3x^2dx$ $=\frac{1}{2}\int\limits_1^9\sqrt{y}\frac{dy}{3}=\frac{1}{6}\cdot\frac{2}{3}y^{3/2}|_{1}^{9}=\frac{1}{9}(27-1)=\frac{26}{9}$

5. anonymous

thank you so much! can you help me on one more with average value please? a function f(t)=6+cos(t/10)=3sin(7t/40), is used to model the velocity of a plane in miles per minute. according to this model, what is the average velocity of the plane for 0 less than or equal to "t" less than or equal to 40?