For the following exercises, evaluate the line integrals using the Fundamental Theorem of Line Integrals. 114. [ T] ∮ c [ arctan y x − x y x 2 + y 2 ] d x + [ x 2 x 2 + y 2 + e − y ( 1 − y ) ] d y , where C is any smooth curve from (1, 1) to (-1,2)
For the following exercises, evaluate the line integrals using the Fundamental Theorem of Line Integrals. 114. [ T] ∮ c [ arctan y x − x y x 2 + y 2 ] d x + [ x 2 x 2 + y 2 + e − y ( 1 − y ) ] d y , where C is any smooth curve from (1, 1) to (-1,2)
For the following exercises, evaluate the line integrals using the Fundamental Theorem of Line Integrals.
114.
[
T]
∮
c
[
arctan
y
x
−
x
y
x
2
+
y
2
]
d
x
+
[
x
2
x
2
+
y
2
+
e
−
y
(
1
−
y
)
]
d
y
,
where C is any smooth curve from (1, 1) to (-1,2)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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