Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero. Then evaluate the line integral. F ( x , y ) = x x 2 + y 2 i + y x 2 + y 2 j , C is the parabola y = 1 + x 2 from ( − 1 , 2 ) to ( 1 , 2 )
Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero. Then evaluate the line integral. F ( x , y ) = x x 2 + y 2 i + y x 2 + y 2 j , C is the parabola y = 1 + x 2 from ( − 1 , 2 ) to ( 1 , 2 )
Solution Summary: The author explains that the line integral of F over C is positive, negative, or zero by using a graph of the vector field.
Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero. Then evaluate the line integral.
F
(
x
,
y
)
=
x
x
2
+
y
2
i
+
y
x
2
+
y
2
j
,
C is the parabola
y
=
1
+
x
2
from
(
−
1
,
2
)
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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