Find the average value of the following function:
$p(x) = 2x^2 + 5x + 2$
on the interval $1 \le x \le 3$.
I know that I need to find $u$, $du$, $v$, and $dv$ and set it up into an definite integral but I don't know what to make them to sent up the equation and find the answer. How do you know what to make them? After I come up with the equation I believe I can solve it.
You find the average of a function via applying the following formula:
$\frac {1}{b-a} \int_{a}^{b} f(x) dx$
$\frac {1}{2} \int_{1}^{3} 2x^2+5x+2 dx$
Wolfram says that the integral returns $124/3$, so
$\frac {1}{2}* \frac {124}{3} = 20.667$
The average value $A$ of a function $p$ over the interval $(a,b)$ is given by \begin{align*} A = \frac{1}{b-a}\int_a^b p(x)dx \end{align*} What are your $a$ and $b$ in this situation?
As seen here, the average value is defined by $$\frac{1}{3-1}\int_{1}^{3} 2x^2+5x+2 \; \mathrm{d}x$$ And there is an nice explanaton for why we define it as such.
I think you can integrate this function. Can you continue from here?