Surface Integral Homework: Evaluate ∫∫σ

[Baumer8993]

Homework Statement

Evaluate ∫∫_σ where S is a surface with sides S₁, S₂, and S₃. S₁ is a portion of the cylinder x²+y² = 1 whose bottom S₂ is the disk x²+y² ≤ 1 and whose top S₃ is the portion of the plane z = 1 + x that lies above S₂.

Homework Equations

Surface integrals, and vector calculus.

The Attempt at a Solution

I am more stuck with starting this problem. Do I need to do two surface integrals, or something else? I am just completely lost on what to do here...

 

[Dick]

Homework Statement

Evaluate ∫∫_σ where S is a surface with sides S₁, S₂, and S₃. S₁ is a portion of the cylinder x²+y² = 1 whose bottom S₂ is the disk x²+y² ≤ 1 and whose top S₃ is the portion of the plane z = 1 + x that lies above S₂.

Homework Equations

Surface integrals, and vector calculus.

The Attempt at a Solution

I am more stuck with starting this problem. Do I need to do two surface integrals, or something else? I am just completely lost on what to do here...

What are you integrating over the surface? You can do it by integrating over the three surfaces and adding them or you might replace the surface integral with a volume integral using the divergence theorem if you just need the total over all three surfaces. Just start doing something.

 

[Baumer8993]

I though I could only use the divergence theorem for flux?

 

[Dick]

I though I could only use the divergence theorem for flux?

Of course, if it's not a flux integral then you can't use the divergence theorem. That's why I was asking WHAT you are integrating.