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.
Determine whether the lines
L₁ (t) = (-2,3, −1)t + (0,2,-3) and
L2 p(s) = (2, −3, 1)s + (-10, 17, -8)
intersect. If they do, find the point of intersection.
Convert the line given by the parametric equations y(t)
Enter the symmetric equations in alphabetic order.
(x(t)
= -4+6t
= 3-t
(z(t)
=
5-7t
to symmetric equations.
Find the point at which the line (t) = (4, -5,-4)+t(-2, -1,5) intersects the xy plane.
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