Calculate the flux of the given vector field by evaluating the line integral directly alongthe given curve for the below parts:(a) The vector field is ⃗ F = (x − y)⃗i + x⃗j. The curve is the circle x^2 + y^2 = 1in the xy-plane. Use the parameterization x = cos t and y = sin t.(b) The vector field is ⃗ F = (x − 1)⃗i + y⃗j. The curve is a circle of radius 3centered at (1, 1). The parametric form of this circle is⃗r = (1 + 3 cos t)⃗i + (1 + 3 sin t)⃗j, 0 ≤ t ≤ 2π(c) The vector field is  ⃗F = x⃗i + y⃗j. The curve is the line segment from thepoint (0, 1) to the point (1, 3).

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Calculate the flux of the given vector field by evaluating the line integral directly along
the given curve for the below parts:
(a) The vector field is ⃗ F = (x − y)⃗i + x⃗j. The curve is the circle x^2 + y^2 = 1
in the xy-plane. Use the parameterization x = cos t and y = sin t.
(b) The vector field is ⃗ F = (x − 1)⃗i + y⃗j. The curve is a circle of radius 3
centered at (1, 1). The parametric form of this circle is
⃗r = (1 + 3 cos t)⃗i + (1 + 3 sin t)⃗j, 0 ≤ t ≤ 2π
(c) The vector field is  ⃗F = x⃗i + y⃗j. The curve is the line segment from the
point (0, 1) to the point (1, 3).

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