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Evaluate ∫CF⃗ ⋅dr⃗ .
∫CF⃗ ⋅dr⃗ =
10. Let C be the curve which is the union of two line segments, the
first going from (0, 0) to (-3, 1) and the second going from (-3, 1) to (-
6, 0).
Compute the line integral ∫C−3dy−1dx.
15.Suppose ∇f(x,y)=5ysin(xy)i⃗ +5xsin(xy)j⃗ , F⃗ =∇f(x,y), and C is
the segment of the parabola y=4x2from the point (3,36) to (4,64).
Then
∫CF⃗ ⋅dr⃗
16.Suppose F⃗ (x,y)=(x+4)i⃗ +(3y+2)j⃗ . Use the fundamental theorem
of line integrals to calculate the following.
(a) The line integral of F⃗ along the line segment C from the
point P=(1,0) to the point Q=(4,3).
∫CF⃗ ⋅dr⃗ =
(b) The line integral of F⃗ along the triangle C from the origin to the
point P=(1,0) to the point Q=(4,3) and back to the origin.
∫CF⃗ ⋅dr⃗ =
20.For the vector
field G⃗ =(yexy+5cos(5x+y))i⃗ +(xexy+cos(5x+y))j⃗ , find the line
integral of G⃗ along the curve C from the origin along the x-axis to
the point (5,0) and then counterclockwise around the circumference of
the circle x2+y2=25 to the point (5/2√,5/2√).∫CG⃗ ⋅dr⃗
21.
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