Q 4. Make a chart of all the new nota... [FREE SOLUTION]

Chapter 14: Q 4. (page 1106)

Make a chart of all the new notation in this section, including what each item means in terms you already understand.

Expert verified

The notations are as below:

We need to write down all the new notation in this section, including what each item means.

The chart is a below:

Notation	Meaning, Definition or Theorem
Arc Length $L$	$L (a, b) = {鈭�}_{a}^{b} \|\|r^{'} (t)\|\| d t$
Parametrized Curve	$r (t) = 鉄� x (t), y (t), z (t) 鉄�$
$\|\|r^{'} (t)\|\|$	$\|\|r^{'} (t)\|\| = \sqrt{{(\frac{d x}{d t})}^{2} + {(\frac{d y}{d t})}^{2} + {(\frac{d z}{d t})}^{2}}$
$d s$	$d s = \|\|r^{'} (t)\|\| d t$
Line Integral of Multivariate functions	${鈭�}_{C} f (x, y, z) d s = {鈭�}_{a}^{b} f (x (t), y (t), z (t)) \|\|r^{'} (t)\|\| d t$
Unit Tangent Vector	$T = \frac{r^{'} (t)}{\|\|r^{'} (t)\|\|}$
Line Integral of Vector Field	${鈭�}_{C} F (x, y, z) 路 d r = {鈭�}_{a}^{b} F (x (t), y (t), z (t)) 路 r^{'} (t) d t$
Fundamental Theorem of Line Integral	${鈭�}_{C} F (x, y, z) 路 d r = f (Q) - f (P)$
Work Done along a curve	$W = {鈭�}_{C} F (x, y, z) 路 d r$

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