2. Find the contour integral f,zdz for (a) y is the triangle ABC oriented counterclockwise, where A = 0, B =1+i and C=-2; (b) y is the circle |z-i =2 oriented counterclockwise.

Q: Evaluate the line integral fc (2 + x*y)s, where C is the half circle x + y? = 1 in the upper half…

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Q: Let C be the positively oriented square with vertices 0, 1, 1 + i, i. Evaluate using the definition…

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Q: Compute the line integral (Баллов: 2) Jo ds, Cis the right half of circle x2 + y 16 (counter…

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Q: Let C denote the unit circle centered at the origin in C. 1 + z + z°* dz, 2πί Then where the…

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Q: (a) Let f(2) = (z +4-i) (z+ + 5z³) Using CRT, evaluate the integral f(z (2)dz, where the contour Cis…

A: According to our company policy, we are supposed to answer only one question at a time. For the rest…

Q: Can you show the steps on how to do this integral?

A: Consider the provided question, (3) Evaluate the integral by using the greens theorem,

Q: Let C denote the unit circle centered at the origin in C. Then r 1 |1+z +z** dz , 2ni z²l dz , where…

A: Since you have posted a multiple questions. So,  we will solve only first question  for you. To get…

Q: Use green's theorem to calculate the integral Fdr, F(r, y) = (e* + x²y , e³ – ry² + sen(3) + 2)…

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Q: Evaluate the line integral L(r – y*)dx + (1+ y² + =*)dy, where Cis the circle of radius 2 centered…

A: We have to evaluate the value of the integral

Q: Let C denote the unit circle centered at the origin in C. Then r 1 ||1+ z+ z dz , 2ni ²l dz , where…

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Q: Let CR be the circle of radius R centered at the origin. Use Green's Theorem to find the value of R…

A: ∮ y3 dx+x dyUsing green's   theorem∮P dx+Q dy=∫R∫∂Q∂x-∂P∂y  dAP=y3                  Q=x∂P∂y=3y2…

Q: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: Evaluate the line integral, where C is the given curve. Sc xy² ds, C is the right half of the circle…

A: Use parametric  method to solve

Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

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Q: | Let C be the quarter circle centered at (2,0) that goes from (1,0) to (2, 1). Evaluate the…

A: ∫c y2xdx + 4yxdy=? We know that this form of integral is solved by Green theorem: ∮cP dx+Q…

Q: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…

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Q: Consider the contour integral P. (-2 + 4)² 1 dz where C is the closed contour consisting of the real…

A: In this question, we evaluate the complex integral by using the Cauchy residue theorem. given that…

Q: Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + (…

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Q: Evaluate the line integral, where C is the given curve. Lexy² ds, C is the right half of the circle…

A: Solution: I=∫cxy4ds

Q: Let C denote the unit circle centered at the origin in C. 1 Then |1 + z + z*l° dz, 2πί C where the…

A: Introduction: A complex number has a conjugate. The conjugate of a complex number is determined by…

Q: Let C be the arc of the circle |z| = 2 from z = 2 to z = 2i that lies in the first quadrant. Without…

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Q: 4. Evaluate the line integral / r y* ds where C is the right half of the circle r² + y² = 16.

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Q: Evaluate the line integral g. y³ dx – x²dy, where C is the positively oriented circle of radius 2…

A: Solved below.

Q: Let F(x, y, z) (x - 2)2 + (y – 1)2 = 9, z 0 oriented in the counter-clockwise direction. (y? + z3,…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: =) Compute the integral z dz, where +y is the circle centered at the origin having radius 2,…

A: Integral on positively oriented curve

Q: Evaluate the line integral - y)dz + (1+ } + æ*)dy, where C is the circle of radius 1 centered at the…

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Q: Evaluate the line integral, where C is the given curve. | xy? ds, C is the right half of the circle…

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Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

Q: 3. Evaluate the integral cosh ™z dz, z(z? + 1) Izl=2 where the circle |z| = 2 is described in the…

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Q: Find the integral fc ez dz where C is the circle |z| = 3 in CCD. (z – 1)2(z – 2) %3D -

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Q: Evaluate the double integral // (x² + y² + 3) dA R over R: the circle centred at the origin (0, 0)…

A: Double Integration problem.....

Q: 3z3 + 2 dz =? Y (z – 1)(z² + 9) |z – 2| = 2 7.

A: We have to calculate the contour integral ∮3z2+2z−1z2+9dz, where circle is given by z−2=2. First…

Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dr where C is the line…

A: Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: Evaluate the line integral L(a - )da + (1 + y° + æ")dy, where Cis the circle of radius 2 centered at…

A: We have to evaluate the integral.

Q: (b) Consider F(x, y) = -i+ j, where (x, y) # (0, 0). x²+y2 x2+y2- Without using Green's Theorem,…

A: Consider the provided function,

Q: 3. Evaluate the integral *zp- where C is the circle |2| = 2.

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Q: 15. Evaluate the contour integral e3z I (z+ 2)ªdz where C' is the circle |z| = . 9e6 2 O 27 9e-6 O…

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Q: Evaluate the line integral (x – y°)dæ + (1+ y +z*)dy, where C is the circle of radius 2 centered at…

A: Hint: By green's theorem in a plane  If fx,y,gx,y be continuous in a region E of xy-plane bounded by…

Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

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Q: (3z+1) z'e (b) $1+2 z'e² (a) p- - dz -dz 3 (s + z7)(1– z)z?

A: Evaluate the given two integrals over the circle z=4 (a) Let fz=3z+12zz-12z+5 The singularities of…

Q: An integral expression for the area of the surface generated by rotating the line segment joining…

A: Given that: Points are- (3,1) , (6, 2)

Q: Compute the line integral f, x?dx + y²dy where the path C consists of the arc of the circle x? + y?…

A: Here we solve the given problem of integral.

Q: Let M(x, y) = y - cos y and N(x, y) = x sin y. Use the Green's Theorem to calculate the line…

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Q: Evaluate the line integral, where C is the given curve. Jo xy ds, C is the right half of the circle…

A: Solved below.

Q: Evaluate the line integral Levis where C is the half circle x² + y² = 1, y ≥ 0. x² + y² ds

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Q: (4) (a) Find the contour integral de using the Cauchy integral formula, where C is the positively…

A: As per the policy, we are solving first question. Please repost it and specify which question is to…

Q: 3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively…

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Q: Evaluate the line integral: x dy – y da x² + y² where C is the circle x² + y? = a², a > 0, oriented…

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