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Green's Theorem Examples
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Green's Theorem Examples.
Here we look at two examples using Green's Theorem.
The first says Evaluate ∫ y dx - x dy over the curve which is the positively oriented circle of radius 2 centered at the origin.
The second example is to evaluate ∫(x^2+y^2) dx + (x^2-y^2) dy over the positively oriented triangular region with vertices (0,0), (2,1) and (0,1).
To use Green's theorem there are really three major steps.
1. Identify P and Q from the line integral to calculate the appropriate partial derivatives.
2. Find the bounds for the region over which we want to evaluate the double integral.
3. Lay the smackdown on the double integral!
As always post any questions below!
Thanks for watching!
-dr. dub
Here we look at two examples using Green's Theorem.
The first says Evaluate ∫ y dx - x dy over the curve which is the positively oriented circle of radius 2 centered at the origin.
The second example is to evaluate ∫(x^2+y^2) dx + (x^2-y^2) dy over the positively oriented triangular region with vertices (0,0), (2,1) and (0,1).
To use Green's theorem there are really three major steps.
1. Identify P and Q from the line integral to calculate the appropriate partial derivatives.
2. Find the bounds for the region over which we want to evaluate the double integral.
3. Lay the smackdown on the double integral!
As always post any questions below!
Thanks for watching!
-dr. dub
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