Two Circles integrals
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Two Circles integrals

[From: ] [author: ] [Date: 12-11-29] [Hit: ]
Suppose that integral(C1) F·dr=5 and integral(C2) F·dr=12. Calculate Integral IntegralD (Py −Qx)dA.-Note that C₁ is the boundary of the unit disk and applying Greens Theorem you will integrate over the unit disk.For C₂, it is the boundary of the disk with radius 3 centered at the origin. Applying Greens Theorem,......
C1 given by x^2+y^2 =1and C2 given by x^2+y^2 =9. Assume each is oriented counter-clockwise. Suppose that F = ⟨P, Q⟩ is a continuous vector field such that Py and Qx are continuous on the region D trapped between the two circles.

Suppose that integral(C1) F·dr=5 and integral(C2) F·dr=12. Calculate Integral IntegralD (Py −Qx)dA.

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Note that C₁ is the boundary of the unit disk and applying Green's Theorem you will integrate over the unit disk.

For C₂, it is the boundary of the disk with radius 3 centered at the origin. Applying Green's Theorem, you will integrate over the disk with radius 3 centered at the origin.

The region D is the annulus created by the two disks. Thus, since we given the values of the line integral along each of the curves, we know that

∬(D) (Py - Qx) dA = ∫(C₁) F•dr - ∫(C₂) F•dr = 5 - 12 = -7

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keywords: integrals,Two,Circles,Two Circles integrals
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