Skip to main content \(\require{cancel}\let\vecarrow\vec
\renewcommand{\vec}{\mathbf}
\newcommand{\ihat}{\vec{i}}
\newcommand{\jhat}{\vec{j}}
\newcommand{\khat}{\vec{k}}
\DeclareMathOperator{\proj}{proj}
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\newcommand{\lbm}[1]{#1~\mathrm{lbm} }
\newcommand{\slug}[1]{#1~\mathrm{slug}}
\newcommand{\m}[1]{#1~\mathrm{m}}
\newcommand{\km}[1]{#1~\mathrm{km}}
\newcommand{\cm}[1]{#1~\mathrm{cm}}
\newcommand{\mm}[1]{#1~\mathrm{mm}}
\newcommand{\ft}[1]{#1~\mathrm{ft}}
\newcommand{\inch}[1]{#1~\mathrm{in}}
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\newcommand{\Nm}[1]{#1~\mathrm{N}\!\cdot\!\mathrm{m} }
\newcommand{\kNm}[1]{#1~\mathrm{kN}\!\cdot\!\mathrm{m} }
\newcommand{\ftlb}[1]{#1~\mathrm{ft}\!\cdot\!\mathrm{lb} }
\newcommand{\ftlbf}[1]{#1~\mathrm{ft}\!\cdot\!\mathrm{lbf} }
\newcommand{\inlb}[1]{#1~\mathrm{in}\!\cdot\!\mathrm{lb} }
\newcommand{\lbperft}[1]{#1~\mathrm{lb}/\mathrm{ft} }
\newcommand{\lbperin}[1]{#1~\mathrm{lb}/\mathrm{in} }
\newcommand{\Nperm}[1]{#1~\mathrm{N}/\mathrm{m} }
\newcommand{\kNperm}[1]{#1~\mathrm{kN}/\mathrm{m} }
\newcommand{\kgperkm}[1]{#1~\mathrm{kg}/\mathrm{km} }
\newcommand{\psinch}[1]{#1~\mathrm{lb}/\mathrm{in}^2 }
\newcommand{\pqinch}[1]{#1~\mathrm{lb}/\mathrm{in}^3 }
\newcommand{\psf}[1]{#1~\mathrm{lb}/\mathrm{ft}^2 }
\newcommand{\pqf}[1]{#1~\mathrm{lb}/\mathrm{ft}^3 }
\newcommand{\Nsm}[1]{#1~\mathrm{N}/\mathrm{m}^2 }
\newcommand{\kgsm}[1]{#1~\mathrm{kg}/\mathrm{m}^2 }
\newcommand{\kgqm}[1]{#1~\mathrm{kg}/\mathrm{m}^3 }
\newcommand{\Pa}[1]{#1~\mathrm{Pa} }
\newcommand{\kPa}[1]{#1~\mathrm{kPa} }
\newcommand{\aSI}[1]{#1~\mathrm{m}/\mathrm{s}^2 }
\newcommand{\aUS}[1]{#1~\mathrm{ft}/\mathrm{s}^2 }
\newcommand{\unit}[1]{#1~\mathrm{unit} }
\newcommand{\ang}[1]{#1^\circ }
\newcommand{\second}[1]{#1~\mathrm{s} }
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\newcommand{\gt}{>}
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\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Instructions.
This interactive shows the difference between horizontal and vertical differential elements
\(dA\text{.}\)
Note that for vertical elements, the lower bounding function changes at
\(x = 1\text{,}\) whereas for horizontal strips the bounding functions don’t change over the range of
\(y\text{.}\)
Use the slider to switch to the differential element.
