Show that the value of the integral
∫ [(x^2+3y)dx + (5x-3y^2)dy]
C
where C is the ellipse x^2/a^2+y^2/b^2=1, is twice the area enclosed by C.
The above equation is -
,
where C is the ellipse
Now comparing this equation with green's theorem , we can only solve this question by green's theorem.
Now statement of green's theorem is that ,
...............A)
now this is the green's theorem now we will compare the given equation with the given equation , we will get -
Now putting the value in equation A) , we get our right hand side as -
area of ellipse)
area of given ellipse =
so , our required answer is
which is the twice the area enclosed by C.
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