Question
In: Math
Evaluate the line integral along the given paths. xy ds (a) C: line segment from (0,0)...
Evaluate the line integral along the given paths.
xy ds
(a) C: line segment from (0,0) to (5, 4)
C: counterclockwise around the triangle with vertices (0, 0),
(8, 0), and (0, 2)
Solutions
milcah answered 2 years agoRelated Solutions
Evaluate the line integral along the given paths. xy ds C (a) C: line segment from...
Evaluate the line integral along the given paths.
xy ds
C
(a)
C: line segment from (0, 0) to
(7, 4)
counterclockwise around the triangle with vertices (0, 0),
(8, 0),
and
(0, 4)
Evaluate the line integral, where C is the given curve. C xeyzds, Cis the line segment...
Evaluate the line integral, where C is the given
curve.
C
xeyzds,
Cis the line segment from
(0, 0, 0) to (2, 3, 4)
Evaluate the line integral, where C is the given curve, where C consists of line segments...
Evaluate the line integral, where C is the given curve, where C
consists of line segments from (1, 2, 0) to (-3, 10, 2) and from
(-3, 10, 2) to (1, 0, 1).
C zx dx + x(y − 2) dy
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = xy i + yz j + zx k
S is the part of the paraboloid
z = 6 − x2 − y2 that lies above the square
0 ≤ x ≤ 1, 0 ≤ y ≤ 1,
and has...
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i − z j + y k
S is the part of the sphere
x2 + y2 + z2 = 1
in the first octant, with orientation toward the origin
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i − z j + y k
S is the part of the sphere
x2 + y2 + z2 = 9
in the first octant, with orientation toward the origin
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral
S
F ·
dS for the given
vector field F and the oriented surface
S. In other words, find the flux of F
across S. For closed surfaces, use the positive (outward)
orientation.
F(x, y, z) =
xzey i −
xzey j + z
k
S is the part of the plane x + y +
z = 3 in the first octant and has downward orientation
Evaluate the surface integral S F · dS for the given vector field F and...
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i + y j + z4 k
S is the part of the cone z =
x2 + y2
beneath the plane
z = 1
with downward orientation
Evaluate the line integral C F · dr, where C is given by the vector function...
Evaluate the line integral
C
F · dr,
where C is given by the vector function
r(t).
F(x, y, z) = sin(x) i + cos(y) j + xz k
r(t) = t5 i − t4 j + t k, 0 ≤ t ≤ 1
Evaluate the surface integral. Double integral x dS, S is the triangular region with vertices (1,...
Evaluate the surface integral.
Double integral x dS, S is
the triangular region with vertices (1, 0, 0), (0, −2, 0), and (0,
0, 6).
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