00:01
In this question we are asked to evaluate the line integration f vector.
00:04
Dr vector along the path c.
00:07
Here path c is a circle of radius 1 centered at the origin.
00:12
Here due to circle, path c is a close path and by using stokes theorem line integration of f vector .d .r.
00:24
Vector along the close path c is given by double integration of curl of f vector dot d s vector.
00:37
Now in part a, circle c present in the xy plane, that means ds vector is equal to dx into dy k k, kp.
00:51
And equation of this circle in the xy plane is given by x square plus y square equals to 1.
00:58
In the parametric form, the equation of this circle is given by x equals to 1.
01:04
1 cos theta and y equals to 1 sine theta.
01:10
Now after putting the value of curl f and ds vector here, this integration will become equals to double integration.
01:18
Dot product of curl of f vector and ds vector is equals to 5 dx, d ,y.
01:28
It is equal to 5 double integration dx, dy over the region r.
01:37
Here region r is the region bounded by the circle...