# Math Help - 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 ... $\textcolor{red}{V = \pi \int_a^b [f(x)]^2 \, dx}$

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

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

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

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

?

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

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

?
correct ... forgot my pi

thanks
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8809429407119751, "perplexity": 786.3772074464482}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246637979.29/warc/CC-MAIN-20150417045717-00018-ip-10-235-10-82.ec2.internal.warc.gz"}