Question

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.

Answer #1

(1 point)
Evaluate the line integral ∫CF⋅dr∫CF⋅dr, where F(x,y,z)=3xi+4yj-zk
and C is given by the vector function r(t)=〈sint,cost,t〉,
0≤t≤3π/2.

Evaluate the line integral ∫F⋅d
r∫CF⋅d r where
F=〈sinx,−3cosy,5xz〉 and C is the path given by
r(t)=(-2t^3,-3t^2,3t) for 0≤t≤1

(1 point) Evaluate the line integral ∫F⋅d r∫CF⋅d r where
F=〈-5sinx,-2cosy,10xz〉 and C is the path given by
r(t)=(2t^3,-3t^2,-2t) for 0≤t≤10≤t≤1
∫F⋅d r=

] Evaluate the surface integral
SF∙dS for the
vector field
Fx,y,z=xi+yj+zk
, where S is the surface given by
z=1-x2-y2,
z≥0 , where S has the positive (outward)
orientation.
Note: SF∙N
dS=RF∙-gxx,yi-gyx,yj+kdA

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

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.

Use Stokes' Theorem to evaluate the integral
∮CF⋅dr=∮C8z^2dx+8xdy+2y^3dz where C is the circle x^2+y^2=9 in the
plane z=0 .

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...

Evaluate the line integral, where C is the given
curve.
xyeyz dy, C: x =
2t, y =
4t2, z =
3t3, 0 ≤ t ≤ 1
C

Evaluate the line integral, where C is the given
curve.
xyeyz dy, C: x =
2t, y =
2t2, z =
3t3, 0 ≤ t ≤ 1
C

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