Question

Consider the vector field F(x, y) = (x ? y) i + xy j, and the curve C where C is the arc of the circle x^2 + y^2 = 4 traversed counterclockwise from (2, 0) to (0, -2). a) Use the graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero. b) Evaluate the line integral ?_C F . dr.

          Consider the vector field F(x, y) = (x ? y) i + xy j, and the curve C where C is the arc of the circle x^2 + y^2 = 4 traversed counterclockwise from (2, 0) to (0, -2).

a) Use the graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero.

b) Evaluate the line integral ?_C F . dr.

Consider the vector field F(x, y) = (x ? y) i + xy j, and the curve C where C is the arc of the circle x^2 + y^2 = 4 traversed counterclockwise from (2, 0) to (0, -2).

a) Use the graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero.

b) Evaluate the line integral ?C F . dr.

Added by Amanda R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

03/22/2022

Step 1

From the graph, we see that the line integral is positive in the 1st and 2nd quadrants, but negative in the 3rd quadrant. However, the negative part in the 3rd quadrant is less than the positive part in the 2nd quadrant. ** Show more…

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Consider the vector field F(x,y) = (x-y) i + xy j, and the curve C where C is the arc of the circle x^2 + y^2 = 4 traversed counterclockwise from (2,0) to (0, -2). a) Use the graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative or zero. b) Evaluate the line integral âˆ«C F.dr.