Question

given field F =[x+y, 2xy ] and c: x= y^2

calculate the line integral along (1,-1) to (4,2)

Answer #1

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)

Compute the line integral 2xy dx + x^2 dy along the following
curves. (a) C1 along the circle x 2 + y 2 = 1 from the point (1, 0)
to (0, 1) using x = cost, y = sin t. (b) C2 along the line x + y =
1 from (0, 1) to (1, 0). (c) C = C1 + C2 for the curves C1 and C2
in parts (a) and (b).

Evaluate the line integral F * dr where F = 〈2xy, x^2〉 and the
curve C is the trajectory of rt = 〈4t−3, t^2〉 for −1 ≤ t≤1.

Consider the vector field below: F ⃗=〈2xy+y^2,x^2+2xy〉 Let C be
the circular arc of radius 1 starting at (1,0), oriented counter
clock wise, and ending at another point on the circle. Determine
the ending point so that the work done by F ⃗ in moving an object
along C is 1/2.

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).

1.
if F(x,y) = ye^x + e^x. find the integral over C of F * dr when C
consists of the line segments 0,1) to (0,2) and (0,2) to
(4,2)

2. Consider the line integral I C F · d r, where the vector
field F = x(cos(x 2 ) + y)i + 2y 3 (e y sin3 y + x 3/2 )j and C is
the closed curve in the first quadrant consisting of the curve y =
1 − x 3 and the coordinate axes x = 0 and y = 0, taken
anticlockwise.
(a) Use Green’s theorem to express the line integral in terms of
a double...

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 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

Given the force field F(x, y) = (x − y, 4x + y^2 ), find the
work done to move along a line segment from (0, 0) to (2,0), along
a line segment from (2,0) to (0,1), and then along another line to
the point (−2, 0). Show your work.

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