| Use the Cauchy integral formulas to evaluate the eiz COS Z -dz, 2²(2z – 37)* where C is the region covered by circle |2 – 2| = 3.

Q: Apply Green's Theorem to evaluate the integral (6y² dx + 6x² dy), where C is the triangle bounded by…

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Q: Q3) Calculate the following integrals over the given C curves by using the Cauchy integral formula.…

A: Part (3):-  Given information Sub-part (a):- ∮e-zz2+π24 dz        C:z-i=1  circle Sub-part (b):-…

Q: Use Green's theorem to evaluate f, xy?dx + 3 cos ydy where C is the boundary of the region in the…

A: Let R be a region in the xy-plane that is bounded by a closed, piecewise smooth curve C, and let…

Q: sin z (a) ? (z-1/6) dz C /z| = 1

A: To answer the given questions we shall use the Cauchy integral formula for higher order derivative…

Q: Use Green's Theorem to evaluate the line integral of F = = (x³,9x) around the boundary of the…

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Q: Use an appropriate transformation to eval- ate the integral /, sin(1 + 9y°) drdy 1 = I D -hen D is…

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Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise (6x…

A: Greens theorem:∫CPdx+Qdy=∫∫R∂Q∂x-∂P∂ydxdy, where R is the region bounded by the simple closed curve…

Q: 5) Evaluate the integral (e* - y) dx + (sin y + x)dy using Green's theorem where Cis bounded by y =…

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Q: Apply Green's Theorem to evaluate the integral. (4y + x)dx + (y + 3x)dy C: The circle (x-6)² + (y -…

A: We have to find the value of integralFor this we using green theoremThe green theorem says that

Q: use Green's theuvem to evaluate the line integral foc xp²x dx + § x ²2³² * √x + ( x² + 2x²y²) dy for…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. (3y +…

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Q: Evaluate (262 + y²) ds, C is the left half of the circle with radius 6 centered at (0,0) and is…

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Q: (a) Let f(z) = 1 - 2i)(24 – 23) - 2 Using CRT, evaluate the integral Of(2)dz, where the contour C is…

A: 1. The point z=a is said to be an isolated singularity if there exists a number such that f(z) is…

Q: Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a…

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Q: Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i +…

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Q: Compute the integral |(5y + pz2020, ) dx + (19x – e-4ycos(v) sin y) dy over the portion of the…

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Q: Verify the Green's theorem for the following integral O sinydx + (x – cosy)dy where curve C is the…

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