Worksheet: Line Integrals of Vector Fields

In this worksheet, we will practice finding the line integral of a vector field along an oriented piecewise differentiable curve in the plane.

Q1:

Calculate for the vector field and curve , where , , , and .

  • A
  • B0
  • C
  • D
  • E

Q2:

Calculate for the vector field and curve , where and is the polygonal path from to to to .

  • A0
  • B
  • C
  • D
  • E

Q3:

Calculate 𝑓 𝑟 𝐶 d for the vector field 𝑓 ( 𝑥 , 𝑦 ) and curve 𝐶 , where 𝑓 ( 𝑥 , 𝑦 ) = 𝑖 𝑗 , 𝐶 𝑥 = 3 𝑡 : , 𝑦 = 2 𝑡 , and 0 𝑡 1 .

Q4:

Calculate for the vector field and the curve , , , .

  • A
  • B
  • C
  • D
  • E

Q5:

Calculate for the vector field and curve , where , , , and .

Q6:

Calculate for the vector field and curve , where , , , and .

Q7:

Calculate for the vector field and curve , where ; , , .

  • A0
  • B
  • C
  • D
  • E

Q8:

Suppose is the path given by for , is the path given by for , and . Without calculating the integrals, which of the following is true?

  • A
  • B
  • C

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