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Statements
∫
𝐜
𝐅
⋅
d
𝐬
=
∫
a
b
𝐅
(
𝐜
(
t
)
)
⋅
𝐜
′
(
t
)
d
t
=
∫
a
b
(
F
1
d
x
d
t
+
F
2
d
y
d
t
+
F
3
d
z
d
t
)
d
t
=
∫
𝐜
F
1
d
x
+
F
2
d
y
+
F
3
d
z
.
subscript
𝐜
⋅
𝐅
𝐬
subscript
superscript
𝑏
𝑎
⋅
𝐅
𝐜
𝑡
superscript
𝐜
′
𝑡
𝑡
subscript
superscript
𝑏
𝑎
subscript
𝐹
1
derivative
𝑥
𝑡
subscript
𝐹
2
derivative
𝑦
𝑡
subscript
𝐹
3
derivative
𝑧
𝑡
𝑡
subscript
𝐜
subscript
𝐹
1
𝑥
subscript
𝐹
2
𝑦
subscript
𝐹
3
𝑧
{\displaystyle{\displaystyle\int_{\mathbf{c}}\mathbf{F}\cdot\mathrm{d}\mathbf{%
s}=\int^{b}_{a}\mathbf{F}(\mathbf{c}(t))\cdot\mathbf{c}^{\prime}(t)\mathrm{d}t%
=\int^{b}_{a}\left(F_{1}\frac{\mathrm{d}x}{\mathrm{d}t}+F_{2}\frac{\mathrm{d}y%
}{\mathrm{d}t}+F_{3}\frac{\mathrm{d}z}{\mathrm{d}t}\right)\mathrm{d}t=\int_{%
\mathbf{c}}F_{1}\mathrm{d}x+F_{2}\mathrm{d}y+F_{3}\mathrm{d}z.}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
F
j
subscript
𝐹
𝑗
{\displaystyle{\displaystyle F_{j}}}
