Worksheet 33
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The Integral Theorems 1. Let C be the curve in R 2 consisting of line segments from (4, 1) to (4, 3) to (1, 3) to (1, 1). Let ~ F (x, y)= x + y, (y - 1) 3 e sin y . Evaluate the line integral Z C ~ F · d~ r. 1 2 3 4 x 1 2 3 4 y 2. Let C be the (oriented) curve parameterized by ~ r(t)= hcos t, sin t, ti,0 ≤ t ≤ 2π. Let ~ F (x, y, z)= he x 2 , (sin y + 3) y ,z 2 i. Evaluate Z C ~ F · d~ r. 1
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Transcript of Worksheet 33
The Integral Theorems
1. Let C be the curve in R2 consisting of line segments from (4, 1) to (4, 3) to (1, 3) to (1, 1). Let
~F (x, y) =⟨x+ y, (y − 1)3esin y
⟩. Evaluate the line integral
∫C
~F · d~r.
1 2 3 4x
1
2
3
4y
2. Let C be the (oriented) curve parameterized by ~r(t) = 〈cos t, sin t, t〉, 0 ≤ t ≤ 2π. Let ~F (x, y, z) =
〈ex2
, (sin y + 3)y, z2〉. Evaluate∫C
~F · d~r.
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