Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate ∫ c F ⋅ d r . F ( x , y ) = x i + y j C : r ( t ) = ( 3 t + 1 ) i + t j , 0 ≤ t ≤ 1
Solution Summary: The author calculates the value of displaystyleundersetCintF.dr if F(x,y)=xi+yj for
Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate
∫
c
F
⋅
d
r
.
F
(
x
,
y
)
=
x
i
+
y
j
C
:
r
(
t
)
=
(
3
t
+
1
)
i
+
t
j
,
0
≤
t
≤
1
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.
Flux of a vector field?
Let S be a closed surface consisting of a paraboloid (z = x²+y²), with (0≤z≤1), and capped by the disc (x²+y² ≤1) on the plane (z=1). Determine the flow of the vector field F (x,y,z) = zj − yk, in the direction that points out across the surface S.
Using Green's Theorem on this vector field problem, compute a) the circulation on the boundary of R in terms of a and b, and b) the outward flux across the boundary of R in terms of a and b.
Using Gauss' theorem to calculate the flow of the vector field 3x3 F: F (x, y, z) = (x^2z, 2x^2, 3z^2) exiting the cylinder defined from the relations x ^2+y ^2<=1, 1<= z <= 2.
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