Respuesta :
30(1-cos2) is the evaluated line integral along the given positively oriented curve.
What is Green's Theorem?
Green's theorem is mostly utilized to evaluate the line integral of a single direction and a curved plane. The link between a line integral and a surface integral is demonstrated by this theorem. It is connected to several theorems, including the Gauss theorem and the Stokes theorem.
To integrate the derivatives in a certain plane, one uses Green's theorem. This thesis can be employed to transform a given line integral into a surface integral, double integral, or conversely.
One of the four calculus foundational theorems, all 4 of whom are intimately connected to one another, is the Green's theorem.
How to solve?
By Green's theorem, we have
∫c (cist dx + x² siny dy ) = ∫∫r [μ(x²siny)/μx - μcosy/μy dxdy
where C is the *boundary* of the rectangle .
The integral is then
=(cos0 -cos2)∫(5,5)(2x +1)dx
=(1-cos2)(5²+5)
=30(1-cos2)
To learn more about green's theorem, visit:
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