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In the following problems, the surface S is the part of the paraboloid z= x^2 +...

In the following problems, the surface S is the part of the paraboloid z= x^2 + y^2 which lies below the plane z= 4, and includes the circular intersection with this plane. This single surface S could also be described as being contained inside the cylinder x^2+y^2= 4.

(a) Iterate, but do not evaluate, the integral ∫∫S(z+x) dS in terms of two parameters. Write the integrand in simplest form.

(b) Use Stoke’s theorem to rewrite ∫S(delta X F) · ndS as a line integral, where F(x, y, z) = xzi + yzj + xyk. Then evaluate this integral.

Math   Advanced-Math   
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Answer #1

In part a I use polar coordinate to write the integral in simple form. And part b can be easily solved by using divergence their.

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