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October 6th, 2017, 12:50 AM   #1
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Joined: Sep 2017
From: Sydney

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Green's Theorem Problem

Need some steps and the solution

Use Green's theorem to show that the area of a region R bounded by the
closed curve C is given by

Check the attachment
Attached Images
 Green Theorm.JPG (13.8 KB, 2 views)

 October 6th, 2017, 01:37 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,100 Thanks: 1093 Green's theorem states $\displaystyle \int \int_R \left(\dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y}\right) = \int_C~P~dx + Q~dy$ let $P=0,~Q=x$ $\dfrac{\partial Q}{\partial x} =1,~\dfrac{\partial P}{\partial y}=0$ $\dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y}=1$ $\displaystyle \int\int_R ~1~ dA = \int\int_R ~\dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y}~dA = \int_C (0)dx + (x)dy = \int_C x ~dy$ I leave you to find $P,~Q$ that allows you to get the other form they ask for Thanks from Country Boy

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