Evaluate the line integral ∫ f. dr by evaluating the surface integral in stokes' theorem with an appropriate choice of s. assume that c has a counterclockwise orientation when viewed from above and will spin clockwise when viewed from below.

f= (6y,-z, x)
c is circle x^2+y^2=20 in the plane z=0

Stokes' theorem allows for any choice of with as its boundary. The simplest region would be the disk in the plane , which can be parameterized using polar coordinates by

with and . Take the normal vector to to be

Then by Stokes' theorem,

where denotes the curl of . The curl is

so the line integral has a value of

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step-by-step explanation:

we need the options

step-by-step explanation: