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line-integral.tex

@@ -86,42 +86,38 @@ $$L=1.47894$$
 
 There are two kinds of line integrals, one for scalar fields and the other
 for vector fields.
-Both are closely related to arc length, as the following table shows.
+Both are closely related to arc length, as shown in the following table.
+
+\bigskip
 
 \begin{center}
-
-\begin{tabular}{|llll|}
+\begin{tabular}{|lll|}
 \hline
- & & & \\
-& $\quad$
+ & & \\
 & Abstract form
 & Computable form
 \\
- & & & \\
+ & & \\
 Arc length
-&
 & $\displaystyle{\int_C ds}$
 & $\displaystyle{\int_a^b |g'(t)|\,dt}$
 \\
- & & & \\
+ & & \\
 Line integral, scalar field
-&
 & $\displaystyle{\int_C f\,ds}$
 & $\displaystyle{\int_a^b f(g(t))\,|g'(t)|\,dt}$
 \\
- & & & \\
+ & & \\
 Line integral, vector field
-&
 & $\displaystyle{\int_C(F\cdot u)\,ds}$
 & $\displaystyle{\int_a^b F(g(t))\cdot g'(t)\,dt}$
 \\
- & & & \\
+ & & \\
 \hline
 \end{tabular}
-
 \end{center}
 
-\medskip
+\bigskip
 \noindent
 We have
 $$ds=|g'(t)|\,dt$$