Evaluate
∫
C
F
⃗
⋅
d
r
⃗
\displaystyle \int_{{C}}\vec{{{F}}}\cdot{d}\vec{{{r}}}
∫
C
F
⋅
d
r
where
F
⃗
=
<
y
2
z
,
x
y
2
,
x
z
>
\displaystyle \vec{{{F}}}=<{y}^{{2}}{z},{x}{y}^{{2}},{x}{z}>
F
=<
y
2
z
,
x
y
2
,
x
z
>
, and
C
\displaystyle {C}
C
is given by
r
⃗
(
t
)
=
<
9
,
t
3
,
t
>
\displaystyle \vec{{{r}}}{\left({t}\right)}=<{9},{t}^{{3}},{t}>
r
(
t
)
=<
9
,
t
3
,
t
>
,
0
≤
t
≤
3
\displaystyle \ {0}\le{t}\le{3}
0
≤
t
≤
3
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