Surface Integrals – On a cone – Exercise 4103

Exercise

Calculate the integral

SPdydz+Qdxdz+Rdxdy\int\int_S Pdydz + Qdxdz +Rdxdy

Where

P=y,Q=x,R=0P=y, Q=-x, R=0

And the surface S is the outside of the half cone

z2=x2+y2,0z3z^2=x^2+y^2, 0\leq z\leq 3

Final Answer

SFn^ds=0\int\int_S \vec{F}\hat{n}ds=0

Solution

Coming soon…

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