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Mathematics
Mathematics
Problem
Evaluate
∫
C
∇
f
⋅
d
r
\int_C \nabla f \cdot d\mathbf{r}
∫
C
∇
f
⋅
d
r
, where
f
(
x
,
y
,
z
)
=
x
y
2
z
+
x
2
f(x, y, z) = xy^2z + x^2
f
(
x
,
y
,
z
)
=
x
y
2
z
+
x
2
and
C
C
C
is the curve
x
=
t
2
,
y
=
e
t
−
1
,
z
=
t
2
+
t
,
−
1
≤
t
≤
1
x = t^2, y = e^{t-1}, z = t^2 + t, -1 \le t \le 1
x
=
t
2
,
y
=
e
t
−
1
,
z
=
t
2
+
t
,
−
1
≤
t
≤
1
.
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