Vault Of Euclid

Surface Integral of a Scalar Function over a Closed Cylinder

Multivariable calculus core

Calculate the surface integral \(\iint_S (x-y)\,dS\), where \(S\) is the cylinder \(x^2+y^2=1\), \(0 \le z \le 2\), including the circular top and bottom.
surface-integralscalar-functioncylindercylindrical-coordinatespolar-coordinatessymmetrymultivariable-calculuscalculus-iiiintegrationdouble-integralparameterizationclosed-surfaceevaluate-integral

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What this problem tests

Tests the ability to parameterize different parts of a piecewise-smooth surface and evaluate the corresponding surface integrals.

This problem is typical of a multivariable calculus course when introducing surface integrals of scalar functions.

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