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Surface Integrals – On a closed domain – Exercise 4782

Exercise

Let E be the bounded area between the XY plane and the surface

z=4-x^2-y^2

Let S be the surface area of E.

Calculate the integral

\int\int_S F\cdot\hat{n} ds

Or in another notation

\int\int_S F\cdot N dA

Where the vector field F is

F=(xz\sin(yz)+x^3,\cos(yz),3zy^2-e^{x^2+y^2})

Final Answer

\int\int_S F\cdot\hat{n} ds=32\pi

Solution

Coming soon…

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