Let n be the outer unit normal (normal away from the origin) of the parabolic shell
S: \(\displaystyle 4x^2 + y + z^2 = 4,y \ge 0\)
and let
F=\(\displaystyle \left\langle { - z + \frac{1}{{2 + x}},\tan ^{ - 1} y,x + \frac{1}{{4 + z}}} \right\rangle\)
Find the value of \(\displaystyle \int {\int {\nabla \times F \cdot nd\sigma } }\)
Help! I'm guessing I'd have to computer the line integral(?) but I don't know how to parametrize this.
Thanks!
S: \(\displaystyle 4x^2 + y + z^2 = 4,y \ge 0\)
and let
F=\(\displaystyle \left\langle { - z + \frac{1}{{2 + x}},\tan ^{ - 1} y,x + \frac{1}{{4 + z}}} \right\rangle\)
Find the value of \(\displaystyle \int {\int {\nabla \times F \cdot nd\sigma } }\)
Help! I'm guessing I'd have to computer the line integral(?) but I don't know how to parametrize this.
Thanks!