Evaluate the following contour integrals 2+1 dz where T is a positively-oriented circle of radius 1 centered at the origin 42 +3 dz where P is a positively- oriented circle of radius 2 centered at the origin. 22+ dz where I is a negatively-oriented circle of radius 2 centered at z = 3 22

Q: 6. Let C be the positively oriented circle centered at the origin with radius Without evaluating the…

A: We will use the principal branch of logarithm

Q: Use Green's Theorem to evaluate the following line integral. i dy -g dx, where (f.g) = (7x,8y) and C…

A: We have,

Q: t C be the circle of radius 4 from 0 to pi/2.  What is the integral around C of  |z|2?   z=x+iy

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Q: evaluate the integral where c circle of positive rotation e^z/1 -cos(z) dz where C is |Z |= 1

A:

Q: The area of the surface obtained by revolving the curve x= Vy+3 for a-3.) 2x /4y + 12 dy 2л уу +3 dy…

A: Consider the curve x=y+3 for a≤y≤b. Find the area of surface when curve is rotated about y-axis.…

Q: Set up, but do not evaluate, an integral for the length of the curve, L. y=cos(x), 0 less then or…

A: Given that,

Q: Use Green's theorem to evaluate the following: (Зу — х3)dx + (6х + у*) dy C where C is the boundary…

A: Green's theorem states that: ∫CPdx+Qdy=∫∫D∂Q∂x-∂P∂ydA Here, P=3y-x3Q=6x+y4 Then, Py=3Qx=6 Using…

Q: Evaluate the integral, where R is the disc with center at the origin and radius 4. 2 cos + - y² ) dA

A:

Q: Find the area of the surface generated by e+ey ey+ e-y revolving the curve x = in the interval 0sys…

A:

Q: (b) Use the following formulas to set up two integrals for the arc length from (0, 0) to (1, 1).…

A: Given query is to find the length of the curve from (-27,9) to (8,4).

Q: Use Green's Theorem to evaluate the following line integral. f dy-g dx, where (f.g) = (x,10y) and C…

A:

Q: Suppose C is the circle r(t) = ⟨cos t, sin t⟩, for 0 ≤ t ≤ 2π,and F = ⟨1, x⟩. Evaluate ∫C F ⋅ n ds…

A:

Q: ( xv – 1) dz х(у —

A: Given that, From the problem, we can understand that x and y are real and imaginary parts of the z…

Q: Set up, but do not evaluate, the integral to find the area of the surface generated when the curve y…

A:

Q: Given the double integral tan y dA, where R is a triangular region in the second quadrant bounded by…

A: Here R is the region of integration bounded by y=0,y=π/4, x=0 and y=-x In the diagram below, OAB is…

Q: Evaluate the line integral by the two following methods. y) dx + (x + y) dy C is counterclockwise…

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Q: $. ay?dx + bxydy

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Q: (b) Use the following formulas to set up two integrals for the arc length from (0, 0) to (1, 1).…

A:

Q: Use the following formula to calculate the area of the region. Area enclosed by C = х dy — у dx, the…

A: Here,

Q: Evaluate the following contour integrals along the given path: (a) Sdz where C is an arc of circle z…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Evaluate the integrals C f (z) dz, where C is the unit circle centered at the origin and f (z) is…

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

Q: Use the Surface Area formula to find the Surface Area of each Rotated figure along the given…

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Q: Evaluate the given integral, where CC is the circle with positive orientation: 2-32 dz Sc C: 12 +…

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Q: Evaluate the integral Ur (x² – 2y²) dA, where R is the first quadrant region between the circles of…

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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: E Use Green's Theorem to evaluate the following integral, (et + 28y³) dx + (6y – 28x³) dy where C is…

A: Let's see where Green's theorem is applicable. Green's theorem is applicable to closed region only.

Q: Evaluate the given integral, where C is the circle with positive orientation: #1. Sc 3E dz, C: Iz +…

A: We have to evaluate the following integral - ∫Cz2-3zz+2idzwhere C : z+i = 2

Q: 4. Evaluate the integral 9 f(z) dz, where C is the unit circle centered at the origin D=64 sin(D*z)…

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Q: The calculation of this integral by the use of the green theorem equals (- a(π^2)/2) Using Green's…

A:

Q: Evaluate the integral xy ds, where C is the curve consisting of the portion of the unit circle of…

A: The given integral is ∫Cxy ds where C is the curve consisting of the portion of the unit circle…

Q: Use one of the formulas below to find the area under one arch of the cycloid x = t - sin(t), y = 1 -…

A: Given arch of cycloid, x=t-sin(t), y=1-cos(t)

Q: ots) Evaluate the following contour integrals: Sc (z² – z + 2) dz, C is quarter circle connecting i…

A: Given  ∫(z2-z+2)dz, C is a quarter circle connecting i to 1C∮(z2+z)(z-3i)2, C:|z|=5C

Q: Use Green's Theorem to evaluate the following line integral. Of dy-g dx, where (f,g) = (8x,5y) and C…

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Q: Evaluate the integral p(x? – 2y?) dA ,where R is the fir - quadrant region between the circles of…

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Q: . Let C be the circle of radius 2 centered at z=0. Compute the following integral over C: ze? 2z -…

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Q: Evaluate the following line integral if C is a piece of the circle x2+y? = 4 from (2,0) to (0,2).…

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Q: If C:|z+2|=3 circle then calculate the following (at attachment) integral I1

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Q: Which of the following integrals correctly gives the ae region consisting of all points above the…

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Q: Set up, but do not evaluate, an integral for the length of the curve. x = 5 sin(y), osys 2 dy

A: Recall: Length of the curve ,L = ∫ab 1+f'(y)2 dy

Q: Evaluate the given integral using the Cauchy Integral Formula or theorem. i dz z2 – 4z where y is…

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Q: Evaluate the given integral (2z+1) dz where the contour C is given in the figure,

A: In this question, we use the path for the integral  ∫C(2z+1)dz where C is the path given in the…

Q: Set up but do not evaluate the integral used to find the area of the surface generated by revolving…

A:

Q: Use Green's Theorem to evaluate the following line integral. i dy -g dx, where (f.g) = (7x,8y) and C…

A:

Q: Compute the area of the unit circle by computing the following double integral 1dædy. z² +y?<1

A:

Q: Use one of the formulas below to find the area under one arch of the cycloid x = t - sin(t), y = 1 -…

A: Area under one arch of the cycloid is