Find the work done by F = (x²+y)i+ (y²+x) j+ze²k over the
following paths from (6,0,0) to (6,0,6).
a. The line segment x = 6, y = 0, 0≤≥≤6
b. The helix r(t) = (6cost)i+ (6sint)j+
Ost≤2π
c. The x-axis from (6,0,0) to (0,0,0) followed by the line z = x, y = 0
from (0,0,0) to (6,0,6)
a. Find a scalar potential function f for F, such that F = Vf.
A. x³ +xy+y³ +ze²-²+C
1
Oc. x²+x²y²+y²+c²+C
OE. The vector field F is not conservative.
The work done by F over the line segment is.
b. Find for F.
df
Ο Α.
-sint+cost+
(6,0,6)
(0,0,0)
لا
(6,0,0)
OB. cost+6costsint+sin+/_/
OC.(cost) + costsint+(sin³t)+3t/x-3x
df
OD.
위
9t
=-216 costsint-36 sin2t+216 sin2tcost+36 cos²21+3/x
The work done by F over the helix is.
c. Choose the correct integral below to compute the work done by F along the x-axis from followed by the line z = x.
(6,0,0)
OA. ((x²+y)i+ (y²+x)+zek)-dr+ ((x²+y)i+ (y²+x)j+ze²k)-dr
(6,0,6)
(0,0,0)
(0,0,0)
(6,0,0)
(6,0,6)
OB. ((x²+y)+(x²+x)J+zek)-dr+ ((x²+y) + (y²+x)J+ze²k)-dr
Oc. ((x²+y)1+ (y²+x)1)-dr + (zek)-dr
(0,0,0)
(6,0,0)
(6,0,6)
(6,0,0)
(0,0,0)
(6,0,0)
(0,0,0)
(6,0,6)
(6,0,0)
(0,0,0)
The work done by F over the two curves is.
OD. ((x²+y)1+ (y²+x)J+zo²k)+dr+ ((x²+y)+(y²+x)1+zo²k).dr
OB. x²+xy+y+ze²-e²+C
OD. x²+xy+y+z-e²+C
