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MathVibes on Instagram: "In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula. The Residue Theorem is a powerful tool in complex analysis that simplifies evaluating complex line integrals over closed curves by relating the integral
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Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem. ∮C x^2 y^2 d x x y d y, C consists of the arc of the parabola y=x^2 from (0,0) to (1,1) and the line segments from (1,1) to (0,1) and from (0,1) to (0,0) | Numerade
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