How to find the limit of integration for an ellipse defined as :
It helps me if you use a detail here plus some use of mathcad or Advanced Grapher or some othersoftware
C: The ellipse 4x^2 + y^2 = 4 in xy-plane, counter clockwise when viewed from the above.
In polar coordinates 4x² + y² = 4 then using dividing by 4 gives
x² + y²/4 = 1
ie x² + (y/2)² = 1
x=cos(theta) , y=2sin (theta)
satisfies the relationship and is the polar coordinate reprentation of the ellipse, and the ellipse is traced out by varing theta from 0 to 2Pi, I do not understand what you mean by the rest of the question.
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maimranAuthor Commented:
OK, I put the whole question here now.
This is from CAlculus and Analytic Geometery by Thomas Fenny 9th edition( page 1122 )
Use the surface integral in Stoke's Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
F = x^2 i + 2x j + z^2 k
C: The ellipse 4x^2 + y^2 = 4 in xy-plane, counter clockwise when viewed from the above.
In the solution manual it just use the result as ( I quote from the solution )
the last line is
= 2(Area of the ellispe ) = 4 PI
it means he use the area as 2 PI but how, I want this.
now apply the theorem with the limits 0 to 2Pi and the result comes out quickly. I am sure you can do the rest.
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x² + y²/4 = 1
ie x² + (y/2)² = 1
x=cos(theta) , y=2sin (theta)
satisfies the relationship and is the polar coordinate reprentation of the ellipse, and the ellipse is traced out by varing theta from 0 to 2Pi, I do not understand what you mean by the rest of the question.