80.1k views
4 votes
Which integral applies Green's theorem to calculate the outward flux across the boundary of a region enclosed by a curve?

A) ∬(Pdx + Qdy)
B) ∬(Qdx - Pdy)
C) ∬(Pdx - Qdy)
D) ∬(Qdx + Pdy)

User Beate
by
8.0k points

1 Answer

4 votes

Final answer:

The correct integral for calculating the outward flux using Green's theorem is ∬(Qdx - Pdy), which is option B in the multiple-choice question.

Step-by-step explanation:

The integral that applies Green's theorem to calculate the outward flux across the boundary of a region enclosed by a curve is given by ∫∫(Qdx - Pdy).

Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C. In the context of flux, it states that the circulation around C of a vector field described by components P and Q is equal to the double integral of ∂Q/∂x - ∂P/∂y over the region D. When calculating outward flux, you want to consider the normal component of the vector field, leading to the form ∫∫(Qdx - Pdy), which is option B) in the given question.

User Antares
by
7.6k points