Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
The area around the given curve according to the green theorem is [tex]F. dr = 0[/tex].
According to the statement
we have to find the area enclosed by the simple closed curve that encloses the origin.
So, We know that the
The given equation is
[tex]f(x,y) = \frac{2xyi + (y^{2} - x^{2} ) j}{(x^{2} + y^{2} )^{2} }[/tex]
and
If function is in form of,
[tex]F = Pi + Qj[/tex]
and C is any positively oriented simple closed curve that encloses the origin.
Then,by use of Green's theorem
Do the partial differentiation of the given function
Then
[tex]\frac{dQ}{dx} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}[/tex]
and
[tex]\frac{dP}{dy} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}[/tex]
On substitution in Green's theorem,
We get the value
[tex]F. dr = 0[/tex]
From this it is clear that the area around the given curve is zero.
So, The area around the given curve according to the green theorem is [tex]F. dr = 0[/tex].
Learn more about Green theorem here
https://brainly.com/question/23265902
#SPJ4
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
