Surface Integrals – On a hemisphere – Exercise 4089

Exercise

Calculate the integral

$\int\int_S Pdydz + Qdxdz +Rdxdy$

Where

$P=x, Q=y, R=z$

And the surface S is the outer side of the hemisphere

$x^2+y^2+z^2=16, z\geq 0$

Final Answer

$\int\int_S \vec{F}\hat{n}ds=128\pi$

Solution

Coming soon…

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