I posted some of the same questions on my other post a few days back. Mr. Fantastic helped me but i want to put them on here to start afresh. Please help me understand on how to do these problems. I have to equation and the book right here but i really dont understand it. If you could help me step by step i would really appreciate it!!!!!
1) If F = (3z - sinx)i + (x^2 + e^y)j + (y^3 - cosz)k, use Stoke's theorem to evaluate integral with lower terminal C [ F.dr] where C is given by x=cost, y=sint, z=1; 0<= t <= 2pie
2) Let S be the first-octant portion of the plane x + y + z =1. Verify Stokes' Theorem for the vector field F = y^2i + z^2j + x^2k
THe part i really dont get is how to do the line integral and the conditions of each terminal. Please help
The edges of S are:
xy-plane (z = 0): x + y = 1.
xz-plane (y = 0): x + z = 1.
yz-plane (x = 0): y + z = 1.
So the closed curve is defined by joining the line segments x + y = 1, x + z = 1 and y + z = 1. Integrate F along each of these line segments.
Along the line segment x + y = 1:
1. y = 1 - x and z = 0.
2. dx + dy = 0 => dy = -dx and dz = 0.
Therefore along the line segment x + y = 1:
The integration along the other two line segments is done in a similar way.
You have to go back and extensively revise the basics.