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(UPDATED) Maximize a double integral
Find the positively oriented simple closed surface C, for which the value of the line integral
Sc ((y^3)y)dx  2x^3dy S is the elongated Sintegral symbol
is a maximum.
I was having trouble figuring this out. I was wondering if I have to go back to a possible original function to do this.
I know that Sc Pdx+Qdy = Sc ((y^3)y)dx  2x^3dx So P=(y^3)y and Q=2x^3. So then F(x,y)=[(y^3)y]i + [2x^3]j.
Our teacher said: Hint: First use Green's Theorem. Consider the resulting double integral. How would you maximize it?
So, using Green's Theorem of Sc Pdx+Qdy= SS(QxPy)dA
The partial derivatives are Qx= 6x^{2} and Py= 3y^{2}1
SS(over the domain) (6x^{2}3y^{2}+1)dA
Now according to the teacher, how would you maximize it?
I am not sure how to maximize it because I am thinking it would go to infinity? Any help? Thanks!
Last edited by crybloodwing; 12062018 at 10:26 AM.
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