Surface Integrals – On a cone – Exercise 4120

Exercise

Calculate the integral

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

Where

P=yz,Q=zx,R=xyP=y-z, Q=z-x, R=x-y

And the surface S is the outside of some of the cone

z2=x2+y2,0z4z^2=x^2+y^2, 0\leq z\leq 4

Final Answer

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

Solution

Coming soon…

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