Question

point) Determine whether the line Integral of each vector field (n blue) along the semicircular, oriented path(in red is positive, negative of zero. LLLL Zero Negative : Positive Positive Positive (Click on a graph to enlarge it)

Answer 1

solution (1) As per vector field diagram, we can see that vector fuld is perpendicular to the direction of the wawe at each pont that is ² (?!). I (+) = 0 therefor liue integral is zero. (2) As per rector field diagrams, we see that vector field is opposite to the direction of cure, thus lue nitigral s negative As per diagram, one can see that hun integral is positive in second quadrant bet negative in first quadrant both have same / equal in maghiliat. Thus total lure integral value is zero (4) As por diagram, one can see that lun integral is positive in second quadrant but negative in first quadrant but both have same / equal in magnitude. Thus total lure integral value is Fero (5) the path is along the vector fuld direction, thus line integral value is positive (6) the path is opposite to the direction of vector fire field, this O olive une integral value is negative

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