Question
In: Math
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
Solutions
milcah answered 2 years agoRelated Solutions
Evaluate the line integral ∫_C F⋅dr, where F(x,y,z)=−4sin(x)i+3cos(y)j−4xzk and C is given by the vector function...
Evaluate the line integral ∫_C F⋅dr, where
F(x,y,z)=−4sin(x)i+3cos(y)j−4xzk and C is given by the vector
function r(t)=t^6i−t^5j+t^4k , 0≤t≤1.
Given the line integral ∫c F(r) · dr where F(x, y, z) = [mxy − z3...
Given the line integral ∫c F(r) · dr where
F(x, y, z) = [mxy − z3 ,(m − 2)x2 ,(1 −
m)xz2 ]
(a) Find m such that the line integral is path independent;
(b) Find a scalar function f such that F = grad f;
(c) Find the work done in moving a particle from A : (1, 2, −3)
to B : (1, −4, 2).
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
Q2. Given the line integral C F (r) · dr where F(x,y,z) = [mxy − z3,(m...
Q2. Given the line integral C F (r) · dr where
F(x,y,z) = [mxy − z3,(m − 2)x2,(1 − m)xz2]
∫
(a) Find m such that the line integral is path
independent;
(b) Find a scalar function f such that F = grad f ;
(c) Find the work done in moving a particle from A : (1, 2,
−3) to B : (1, −4, 2).
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 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
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