# Thread: Volume && Average Value Problems.

1. ## Volume && Average Value Problems.

I'm having a little trouble with the following problems and I was wondering if someone could help out with either of them.

1) A football has the shape of the solid generated by revolving the region bounded between the x-axis and the parabola
y = (4R(x^2 - 1/4L^2)^2)/L^2 about the x-axis. Find its volume.

2) Find the average value of f(x) = ex + e-x over the interval [ln ½, ln 2]

Thanks!

2. Originally Posted by Sotellme01
I'm having a little trouble with the following problems and I was wondering if someone could help out with either of them.

1) A football has the shape of the solid generated by revolving the region bounded between the x-axis and the parabola
y = (4R(x^2 - 1/4L^2)^2)/L^2 about the x-axis. Find its volume.

disk method ... $\displaystyle \textcolor{red}{V = \pi \int_a^b [f(x)]^2 \, dx}$

2) Find the average value of f(x) = ex + e-x over the interval [ln ½, ln 2]

$\displaystyle \textcolor{red}{f_{avg} = \frac{1}{b-a} \int_a^b f(x) \, dx}$
...

3. $\displaystyle \textcolor{red}{V = \int_a^b [f(x)]^2 \, dx}$
Is that not supposed to be:

$\displaystyle V = \pi\int_a^b [f(x)]^2 \, dx$
?

4. Originally Posted by hjortur
Is that not supposed to be:

$\displaystyle V = \pi\int_a^b [f(x)]^2 \, dx$
?
correct ... forgot my pi

thanks