October 6th, 2017, 12:50 AM  #1 
Newbie Joined: Sep 2017 From: Sydney Posts: 17 Thanks: 0  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 
October 6th, 2017, 01:37 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,981 Thanks: 1027 
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 

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calculus3, green, problem, theorem, therom 
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