Let n be the outer unit normal (normal away from the origin) of the parabolic shell S: x + y^2 + z^2 = 1, x ? 0 and let F = yi - z(tan^-1 x + 1)j + y^2k. Evaluate the surface integral: ?_S ? × F ? n d?
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We can do this by letting y = y and z = z, and then solving for x in terms of y and z: x = 1 - y^2 - z^2. Now, we can write the position vector r as a function of y and z: r(y, z) = (1 - y^2 - z^2)i + yj + zk. Show more…
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