-#LyX 1.6.5svn created this file. For more info see http://www.lyx.org/
-\lyxformat 345
+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
\begin_document
\begin_header
+\save_transient_properties true
+\origin /systemlyxdir/examples/
\textclass tufte-book
-\options justified
\use_default_options true
+\maintain_unincluded_children false
\language english
+\language_package default
\inputencoding auto
-\font_roman default
-\font_sans default
-\font_typewriter default
+\fontencoding global
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
\font_default_family default
+\use_non_tex_fonts false
\font_sc false
\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures false
\graphics default
+\default_output_format pdf2
+\output_sync 0
+\bibtex_command bibtex
+\index_command default
\paperfontsize default
\spacing single
-\use_hyperref false
+\use_hyperref true
+\pdf_bookmarks true
+\pdf_bookmarksnumbered false
+\pdf_bookmarksopen true
+\pdf_bookmarksopenlevel 1
+\pdf_breaklinks false
+\pdf_pdfborder true
+\pdf_colorlinks false
+\pdf_backref false
+\pdf_pdfusetitle true
\papersize default
\use_geometry true
-\use_amsmath 1
-\use_esint 1
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
\use_bibtopic false
+\use_indices false
\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 0
+\use_minted 0
+\notefontcolor #0000ff
+\index Index
+\shortcut idx
+\color #008000
+\end_index
\secnumdepth 2
\tocdepth 2
\paragraph_separation indent
-\defskip medskip
-\quotes_language english
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
-\author ""
-\author ""
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
\end_header
\begin_body
\begin_layout Plain Layout
\series bold
-Important note:
+Note
\series default
- The menu
-\family sans
-Insert\SpecialChar \menuseparator
-Hyperlinks
-\family default
- and the
+: To be able to view your file as PDF you must have the \SpecialChar LaTeX
+-package
\family sans
-PDF properties
+fpl
\family default
- in the
-\family sans
-Document\SpecialChar \menuseparator
-Settings
-\family default
- menu cannot be used for tufte document classes!
+ installed to your \SpecialChar LaTeX
+ system.
+ If you are using MiK\SpecialChar TeX
+, you will automatically be asked to install this package
+ when previewing your file, if you are using \SpecialChar TeX
+Live, use \SpecialChar TeX
+Live's package manager.
+\end_layout
+
+\begin_layout Plain Layout
+
+\series bold
+Note 2
+\series default
+: If you wish to compile to PDF with plain \SpecialChar LaTeX
+ (instead of pdf\SpecialChar TeX
+), there is currently
+ a bug in the Tufte class that causes errors.
+ You can add the class option 'nols' (put this in the
+\begin_inset Quotes eld
+\end_inset
+
+Custom
+\begin_inset Quotes erd
+\end_inset
+
+ field of Document\SpecialChar menuseparator
+Settings \SpecialChar menuseparator
+Document Class) to get rid of the errors, but
+ this also removes letterspacing, an important part of the Tufte design.
\end_layout
\end_inset
\end_layout
\begin_layout Title
-Random Tufte Examples
+Tufte Examples
\end_layout
\begin_layout Author
\begin_layout Standard
In this document, it was endeavored to show some of the features of the
- Tufte-book class.
+
+\family sans
+Tufte-book
+\family default
+ class.
In the first chapter, their use is outlined.
- In the second chapter, their use through a handout thjat was created in
+ In the second chapter, their use through a handout that was created in
a calculus class is demonstrated.
\end_layout
\end_layout
\begin_layout Standard
-The Tufte-book class is based on the work of Edward Tufte.
- It provides the same functionality as the Tufte-handout class with book-specifi
-c additions.
- Tufte's documents consist of a column of text beside a wide column of margin
- notes and margin figures.
+The
+\family sans
+Tufte-book
+\family default
+ class is based on the work of
+\noun on
+Edward Tufte
+\noun default
+.
+ It provides the same functionality as the
+\family sans
+Tufte-handout
+\family default
+ class with book-specific additions.
+ Tufte's documents consist of a rather narrow column of text and a wide
+ column of margin notes and margin figures.
This is to improve readability.
\end_layout
\begin_layout Standard
-Features included in this format include:
+The features provided by this format include:
\end_layout
\begin_layout Itemize
\begin_layout Standard
In this sample document, some of these features are demonstrated.
- For a full demonstration, visit the tufte-latex webpage:
+ For a full demonstration, visit the tufte-latex website:
\begin_inset Flex URL
status collapsed
\begin_layout Plain Layout
-http://code.google.com/p/tufte-latex
+https://tufte-latex.github.io/tufte-latex/
\end_layout
\end_inset
rather than justified.
\begin_inset Flex Sidenote
-status collapsed
+status open
\begin_layout Plain Layout
-This document is justified.
- Add the option "justified" to the Custom line of the Document Class part
- of the Document Settings.
+To get justified text, add the option
+\emph on
+justified
+\emph default
+ to the
+\emph on
+Custom
+\emph default
+ field in
+\family sans
+Document\SpecialChar menuseparator
+Settings\SpecialChar menuseparator
+Document Class
+\family default
+.
\end_layout
\end_inset
- The ragged right is used in most of his works, but the option exists for
- justified text.
+ Ragged right text is used in most of his works, but the class option
+\emph on
+justified
+\emph default
+ is provided to change this.
\end_layout
\begin_layout Standard
-Tufte also formats his pages so that they are not symmetric.
- Instead, each page is the same and all the marginalia appear on the right
- side of each page.
- After experimentation, I agree that this option is best.
- A symmetric layout appeared strange, to say the least.
+Tufte also formats his pages asymmetrically.
+ This means that the marginalia appear on the right side on each page, whether
+ odd or even.
+ If you prefer, you can change that and have symmetric layout, as common
+ in traditional book typography, by using the
+\emph on
+symmetric
+\emph default
+ class option.
\begin_inset Flex Sidenote
-status collapsed
+status open
\begin_layout Plain Layout
-To create a symmetric layout, add the option "symmetric" to the Custom line
- of the Document Class part of the Document Settings.
+To create a symmetric layout, add the option
+\emph on
+symmetric
+\emph default
+ to the
+\emph on
+Custom
+\emph default
+ field in
+\family sans
+Document\SpecialChar menuseparator
+Settings\SpecialChar menuseparator
+Document Class
+\family default
+.
\end_layout
\end_inset
\end_layout
\begin_layout Standard
-Finally, by default, Tufte does not number his chapters or his sections.
- Since I like to refer to sections by number, I changed this section in
- the Document Settings by moving the slider under the Numbering and TOC
- section.
+Finally, Tufte does not number his chapters or his sections.
+ If you like to refer to sections by number, move the
+\emph on
+Numbering
+\emph default
+ slider in
+\family sans
+Document\SpecialChar menuseparator
+Settings\SpecialChar menuseparator
+Numbering & TOC
+\family default
+ to the very right (as done in this document).
\begin_inset Flex Marginnote
status collapsed
\end_layout
\begin_layout Standard
-Tufte uses ordinary figure floats like this:
+Tufte uses ordinary figure floats such as the following:
\end_layout
\begin_layout Standard
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
status open
\begin_layout Plain Layout
\end_inset
-\begin_inset Caption
+\begin_inset Caption Standard
\begin_layout Plain Layout
An ordinary figure float.
\end_layout
\begin_layout Standard
-Tufte also uses margin figures, a feature I wish I could apply to the Memoir
- class.
+Furthermore, he uses margin figures, as shown in Fig.
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:margin-figure"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace 5theight%
+\end_inset
+
+
\end_layout
\begin_layout Standard
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
status open
\begin_layout Plain Layout
\end_inset
-\begin_inset Caption
+\begin_inset Caption Standard
\begin_layout Plain Layout
-A margin figure
+A margin figure.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:margin-figure"
+
+\end_inset
+
+
\end_layout
\end_inset
\end_layout
\begin_layout Standard
-Naturally, the Tufte-book class also allows the use of tables in the margins
- and in the text in the same way that the figures are used.
- I would use the margin tables for a small set of data to illustrate a concept
- such as
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+\series default
+ If you are using margin figures or tables you must use the default float
+ placement option in the document settings under
+\family sans
+Float
+\begin_inset space ~
+\end_inset
+
+Placement
+\family default
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the same vein, the
+\family sans
+Tufte-book
+\family default
+ class allows the use of tables, both in the margins and in the text.
+ The margin tables are recommended for a small set of data to illustrate
+ a concept such as
\begin_inset Quotes eld
\end_inset
\begin_inset Quotes erd
\end_inset
- I might put flame test results and comments in a full-width table.
+ More detailed data such as flame test results and comments should be put
+ in a full-width table instead.
\end_layout
\begin_layout Standard
-I did attempt to use the figure-wrap float with Tufte.
- LyX interpreted it as a figure float and sometimes didn't show it at all.
- With only the narrow column of text available, I think that it should probably
- be suppressed when someone edits the layout file!
-\end_layout
+Finally,
+\family sans
+Tufte-book
+\family default
+ provides a full-width figure.
+ This one takes up the entire width of the page, i.
+\begin_inset space \thinspace{}
+\end_inset
-\begin_layout Standard
-A final type of figure is a full-width figure.
- This is one which takes up the entire width of the page: text and margin
- alike.
- I'm proud of this because this was my one original contribution as it does
- not seem to be in the Tufte-handout.layout file.
+e., text and margin.
+ See Fig.
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:full-width-figure"
+
+\end_inset
+
+ for an example.
\end_layout
\begin_layout Standard
has_inner_box 1
inner_pos "t"
use_parbox 0
-width "100col%"
+use_makebox 0
+width "100line%"
special "none"
height "1in"
height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
status open
\begin_layout Plain Layout
-Imagine a photograph of a squirrel stretched out on its side in this box.
- One of the bugs in my layout is that this only works with pictures, not
- with frames around minipages, the way it's set up here.
+Imagine your favorite photograph of a squirrel inside this box instead of
+ this boring text.
\end_layout
\end_inset
+\begin_inset VSpace defskip
+\end_inset
+
+
\end_layout
\begin_layout Plain Layout
-\begin_inset Caption
+\begin_inset Caption Standard
\begin_layout Plain Layout
A full-width figure.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:full-width-figure"
+
+\end_inset
+
+
\end_layout
\end_inset
\end_inset
- Alternatively, you can also use directly the sidenote inset.
+ Alternatively, you can also use the
+\family typewriter
+Sidenote
+\family default
+ inset directly; you'll find it in the
+\family sans
+Insert\SpecialChar menuseparator
+Custom Insets
+\family default
+ menu.
\begin_inset Flex Sidenote
status open
\end_inset
innovation is Tufte's
-\series bold
-new thought
-\series default
- command.
- It introduces new thoughts, such as this paragraph, with small capitals.
- To accomplish this, use the
\family typewriter
NewThought
\family default
character style (
\family sans
-Edit\SpecialChar \menuseparator
-TextStyle\SpecialChar \menuseparator
+Edit\SpecialChar menuseparator
+TextStyle\SpecialChar menuseparator
NewThought
\family default
).
+ It introduces new thoughts by means of small caps, as demonstrated in this
+ paragraph.
+
\end_layout
\begin_layout Standard
-The Tufte document classes includes two new character styles and some improvemen
-ts on existing commands for letterspacing.
+The Tufte document classes include two new character styles and some improvement
+s on existing commands for letterspacing.
\end_layout
\begin_layout Standard
status open
\begin_layout Plain Layout
-Small Caps
+small caps
\end_layout
\end_inset
-, the letterspacing---that is, the spacing between the letters---should
- be increased slightly.
+, the letterspacing—that is, the spacing between the letters—should be increased
+ slightly.
\begin_inset CommandInset citation
LatexCommand cite
key "Bringhurst2005"
+literal "true"
\end_inset
\emph default
character style (
\family sans
-Edit\SpecialChar \menuseparator
-TextStyle\SpecialChar \menuseparator
+Edit\SpecialChar menuseparator
+TextStyle\SpecialChar menuseparator
AllCaps
\family default
) has proper letterspacing for strings of
\emph default
character style (
\family sans
-Edit\SpecialChar \menuseparator
-TextStyle\SpecialChar \menuseparator
+Edit\SpecialChar menuseparator
+TextStyle\SpecialChar menuseparator
SmallCaps
\family default
) has letterspacing for
The Initial Letters Of The Words In This Sentence Are Capitalized.
\end_layout
+\begin_layout Standard
+Finally, the
+\emph on
+ Full Width
+\emph default
+ paragraph environment provides a paragraph layout that stretches across
+ the main text block and the sidenotes area:
+\end_layout
+
\begin_layout Full Width
-This is full width text.
- I'm not going to quote a text because I don't want to mess with citations
- and I haven't yet figured out how to use BiBTeX.
- I thought about quoting from some of my own materials, but then I decided
- not to.
- Instead, I decided to just type for a while and fill up 3 lines on my screen
- with whatever nonsense came into my head.
-
+Lorem ipsum dolor sit amet, consectetuer adipiscing elit.
+ Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.
+ Curabitur dictum gravida mauris.
+ Nam arcu libero, nonummy eget, consectetuer id, vulputate a, magna.
+ Donec vehicula augue eu neque.
+ Pellentesque habitant morbi tristique senectus et netus et malesuada fames
+ ac turpis egestas.
+ Mauris ut leo.
+ Cras viverra metus rhoncus sem.
+ Nulla et lectus vestibulum urna fringilla ultrices.
+ Phasellus eu tellus sit amet tortor gravida placerat.
+ Integer sapien est, iaculis in, pretium quis, viverra ac, nunc.
+ Praesent eget sem vel leo ultrices bibendum.
+ Aenean faucibus.
+ Morbi dolor nulla, malesuada eu, pulvinar at, mollis ac, nulla.
+ Curabitur auctor semper nulla.
+ Donec varius orci eget risus.
+ Duis nibh mi, congue eu, accumsan eleifend, sagittis quis, diam.
+ Duis eget orci sit amet orci dignissim rutrum.
\end_layout
\begin_layout Section
-Conclusions
+References
+\end_layout
+
+\begin_layout Standard
+References are placed alongside their citations as sidenotes, as well.
+ This can be accomplished using the normal citation command.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+The previous section includes a citation.
+\end_layout
+
+\end_inset
+
+
\end_layout
\begin_layout Standard
-I like a lot of what Tufte has done.
- At the moment, however, I only use his style in my Calculus class.
- I have a good Calculus book, but it requires extensive notes to adapt it
- for the high school level.
- For my Physics, Chemistry, and Biology courses, the Memoir class seems
- more suited.
- I wish it were possible to take the idea of margin figures from Tufte and
- put it into Memoir.
- I also prefer Tufte's method of dealing with margin notes.
+The complete list of references may also be printed automatically by using
+
+\family sans
+Insert\SpecialChar menuseparator
+Lists/TOC\SpecialChar menuseparator
+Bib\SpecialChar TeX
+
+\begin_inset space ~
+\end_inset
+
+Bibliography
+\family default
+ (see the end of this document for an example.) If you do not want to print
+ a bibliography at the end of your document, place the
+\family sans
+Bib\SpecialChar TeX
+
+\begin_inset space ~
+\end_inset
+
+Bibliography
+\family default
+ inset inside a \SpecialChar LyX
+ note and use the \SpecialChar LaTeX
+ command
+\family typewriter
+
+\backslash
+nobibliography
+\family default
+ the text.
\end_layout
\begin_layout Chapter
-Calculation of Volume: Sections 2.12-2.13
+Calculation of Volume: Sections 2.12–2.13
\end_layout
-\begin_layout Abstract
+\begin_layout Standard
Imagine taking a function like
\begin_inset Formula $y=\sqrt{x}$
\end_inset
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
status open
\begin_layout Plain Layout
\end_inset
-\begin_inset Caption
+\begin_inset Caption Standard
\begin_layout Plain Layout
\begin_inset CommandInset label
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
status open
\begin_layout Plain Layout
\end_inset
-\begin_inset Caption
+\begin_inset Caption Standard
\begin_layout Plain Layout
\begin_inset CommandInset label
.
Since height multiplied by width was the area of each rectangle, we summed
these areas and rewrote this as
-\begin_inset Formula $\int\, f(x)\, dx$
+\begin_inset Formula $\int\,f(x)\,dx$
\end_inset
, or, in this specific case,
-\begin_inset Formula $\int\,\sqrt{x}\, dx$
+\begin_inset Formula $\int\,\sqrt{x}\,dx$
\end_inset
.
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-V=hA\]
+\begin_inset Formula
+\[
+V=hA
+\]
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-A=\pi f^{2}(x)\]
+\begin_inset Formula
+\[
+A=\pi f^{2}(x)
+\]
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
A & = & \pi\left(\sqrt{x}\right)^{2}\\
- & = & \pi x\end{eqnarray*}
+ & = & \pi x
+\end{eqnarray*}
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-V=\pi x\, dx\]
+\begin_inset Formula
+\[
+V=\pi x\,dx
+\]
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-V=\pi f^{2}(x)\, dx\]
+\begin_inset Formula
+\[
+V=\pi f^{2}(x)\,dx
+\]
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\int_{a}^{b}\,\pi f^{2}(x)\, dx\end{equation}
+\begin_inset Formula
+\begin{equation}
+\int_{a}^{b}\,\pi f^{2}(x)\,dx
+\end{equation}
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
-\int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
+\begin_inset Formula
+\begin{eqnarray*}
+\int_{0}^{4}\,\pi x\,dx & = & \pi\int_{0}^{4}\,x\,dx\\
& = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
& = & \pi\left(\frac{4^{2}}{2}-0\right)\\
- & = & 8\pi\end{eqnarray*}
+ & = & 8\pi
+\end{eqnarray*}
\end_inset
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
status open
\begin_layout Plain Layout
\end_inset
-\begin_inset Caption
+\begin_inset Caption Standard
\begin_layout Plain Layout
The functions
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
A_{washer} & = & A_{cup}-A_{drill}\\
& = & \pi f^{2}(x)-\pi g^{2}(x)\\
- & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\end{eqnarray*}
+ & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
+\end{eqnarray*}
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
-V_{washer} & = & A_{washer}\, dx\\
- & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
+V_{washer} & = & A_{washer}\,dx\\
+ & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
+\end{eqnarray*}
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{equation}
+\begin_inset Formula
+\begin{equation}
+\int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\,dx
+\end{equation}
\end_inset
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
status open
\begin_layout Plain Layout
\end_inset
-\begin_inset Caption
+\begin_inset Caption Standard
\begin_layout Plain Layout
The cup with a quadratic hole drilled down its length
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
-\int_{0}^{4}\,\pi\left(\left(\sqrt{x}\right)^{2}-\left(\frac{x^{2}}{16}\right)\right)\, dx & = & \pi\int_{0}^{4}\,\left(x-\frac{x^{4}}{256}\right)\, dx\\
- & = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
+\begin_inset Formula
+\begin{eqnarray*}
+\int_{0}^{4}\,\pi\left(\left(\sqrt{x}\right)^{2}-\left(\frac{x^{2}}{16}\right)\right)\,dx & = & \pi\int_{0}^{4}\,\left(x-\frac{x^{4}}{256}\right)\,dx\\
+ & = & \pi\left(\int_{0}^{4}\,x\,dx-\int_{0}^{4}\,\frac{x^{4}}{256}\,dx\right)\\
& = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
& = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
& = & \pi\left(8-0.8\right)\\
- & = & 7.2\pi\end{eqnarray*}
+ & = & 7.2\pi
+\end{eqnarray*}
\end_inset
projects / lyx.git / blobdiff