Surface integral problem with attached image

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Homework Statement



Please read the attached

Homework Equations




In the image attached

The Attempt at a Solution



Thanks a lot
 
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  • Typeset problem: find a parametrization Φ of the upper half sphere x^2 + y^2 + z^2 = 1 with z >= 0, then evaluate a) the integral over Φ of z dS and b) the integral over Φ of (x + 3y^5, y + 10xz, z - xy) · dS.
    ejer 11.jpg
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  • Typeset problem 2: use Green's theorem to find the area enclosed by a) the ellipse x^2/a^2 + y^2/b^2 = 1 and b) the cycloid x = t - sin t, y = 1 - cos t for t in [0, 2pi].
    ejer 12-2.jpg
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  • Typeset problem 13: verify that the surface integral over S of F dot dS equals the triple integral over V of div F dxdydz, where F = (4x, -2y^2, z^2), V is bounded by cylinder x^2 + y^2 = 4 and planes z = 0 and z = 3.
    ejer 12-3.jpg
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If i were you, and wanted a rsponse, I suggest reposting this over on calculus and beyond, but at least make an effort at showing what you don't understand or do. Otherwise it will be likely ignored as has been here. So iy you can do first part where you make parametric as fx(z), do that, and ask how do I proceed?
 
ok thanks for the advice, the thing is a little problem after I make the variable change.. I ´ll re-post explaining myself better...
 
No Problem, this is a great resource, just need to learn a few ground rules to reap great rewards.