Question

Sketch the vector field vec F (x,y)=xi +yj and calculate the
line integral of along the line segment vec F from (5, 4) to (5,
8)

Answer #1

Sketch the vector field F⃗ (x,y)=−5i and calculate the line
integral of F⃗ along the line segment from (−5,3) to (0,4).

Evaluate the vector line integral F*dr of F(x,y) = <xy,y>
along the line segment K from the point (2,0) to the point (0,2) in
the xy-plane

Find the divergence of the following vector field: C(x, y) = (xi
+ yj) * log((x^2) + (y^2))

given field F =[x+y, 2xy ] and c: x= y^2
calculate the line integral along (1,-1) to (4,2)

Calculate the line integral of the vector field
?=〈?,?,?2+?2〉F=〈y,x,x2+y2〉 around the boundary curve, the curl of
the vector field, and the surface integral of the curl of the
vector field.
The surface S is the upper hemisphere
?2+?2+?2=36, ?≥0x2+y2+z2=36, z≥0
oriented with an upward‑pointing normal.
(Use symbolic notation and fractions where needed.)
∫?⋅??=∫CF⋅dr=
curl(?)=curl(F)=
∬curl(?)⋅??=∬Scurl(F)⋅dS=

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) = −xi − yj + z3k,
S is the part of the cone z =
x2 + y2
between the planes
z = 1
and
z = 2
with downward orientation

Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=5xi+yj−2zk and
C is given by the vector function r(t)=〈sint,cost,t〉, 0≤t≤3π/2.

Consider the vector field F = <2 x
y^3 , 3 x^2
y^2+sin y>. Compute
the line integral of this vector field along the quarter-circle,
center at the origin, above the x axis, going from the point (1 ,
0) to the point (0 , 1). HINT: Is there a potential?

For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a
function f(x, y) such that F~ (x, y) = ∇f(x, y) = h ∂f ∂x , ∂f ∂y i
by integrating P and Q with respect to the appropriate variables
and combining answers. Then use that potential function to directly
calculate the given line integral (via the Fundamental Theorem of
Line Integrals):
a) F~ 1(x, y) = hx 2 , y2 i Z C F~ 1...

the electrostatic force vector F for a system of unit
charges is defined by vector F=(x^2+y^2+z^2)^n (xi+yj+zk). where is
an integer. Find (a) div vector F, (b) a scalar potential psi such
that F =-delta psi. Leave your answer in terms of vector |r| where
vector r=(xi+yj+zk).
the electrostatic force vector F for a system of unit
charges is defined by vector F=(x^2+y^2+z^2)^n (xi+yj+zk). where is
n an integer. Find (a) div vector F, (b) a scalar potential psi
such...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 9 minutes ago

asked 11 minutes ago

asked 12 minutes ago

asked 16 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 27 minutes ago

asked 34 minutes ago

asked 35 minutes ago

asked 50 minutes ago

asked 58 minutes ago