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In this lesson, we will learn how to find 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 .

Q2:

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 curve , where and is the polygonal path from to to to .

Q5:

Q6:

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

Q7:

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

Q8:

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

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