Integral Calculus and Differential Equations using MATHEMATICA by PEREZ LOPEZ CESAR

Author:PEREZ LOPEZ, CESAR
Language: eng
Format: azw3
Published: 2016-01-14T16:00:00+00:00

Exercise 4-14. Use Stokes’ theorem to evaluate the line integral:

where C is the intersection of the cylinder x2 + y2 = 1 and the plane x + y + z = 1, and the orientation of C corresponds to counterclockwise rotation of the OXY plane.

The curve C bounds the surface S defined by z = 1-x-y = f(x,y) for (x, y) in the domain D = {(x,y) / x2 + y2= 1}.

We put F= - y 3 i + x 3 j - z 3 k.

Now, we calculate the curl of F and integrate over the surface S:

In[1]:= F={-y^3,x^3,z^3}

3 3 3

{-y , x , z }

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