1- Assume that x, y ER and z = x + iy e C. Calculate the following integrals on C = {z:|z| = 1} contour. (All integrals are in positive direction.) 4z3 dz

Q: Let a(z, r) := 2+ re", te (0, 27). Calculate the following integrals: a) Sa-a sin(=) dz; sin(s) b)…

A: Given:                    αz,r:=z+reit, t∈0,2π To find: Evaluate the given integrals over the given…

Q: Evaluate the line integral by the two following methods. fwox xy dx + x²y3 dy C is counterclockwise…

A: Since, we have to evaluate the line integral given by:-I=∮C xy dx + x2y3  dy -(i)Our aim is to solve…

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the const 6 + 12y – 36y2 dy 3 + ( 6y…

A: Given ∫y-36y2+12y+6dy⇒6∫y-6y2+2y+1 dy⇒∫y-6y2+2y+1dy , write y as 16-1122-12y and…

Q: Evaluate the double integral f(r, 8) dA. * T/2 (5 cos(8) r dr de T/2 Jo

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Q: 22. Evaluate the iterated integral. (b) f. [, 2x + »)'dy (a) x+y+ xy dydx

A: Now we will solve the given double integral  We know integration of Xn dx = X(n+1) / (n+1) + C ,…

Q: Verify Green's Theorem by evaluating both integrals ON aM | y? dx + -x² dy dA ax ay for the given…

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Q: 1- Assume that x,y ER and z=x+ iy € C. Calculate the following integrals on C = {z:|z] = 1} contour.…

A: Residue theorem: If C is positively oriented simple closed curve and a1, a2,..., an are the point of…

Q: 3. Compute , xe*ydA where R is the rectangle 0 <x< 1,1< y< 2, using iterated integrals in both…

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Q: Evaluate the given line integral. | (y, -x) · dR, where C consists of the uppder part of x2 + y? = 1…

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Q: 1- Assume that x, y € R and z = x + iy € c.Calculate the following integrals using the given contour…

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Q: 2- Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals…

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Q: 1- Assume that x, y ER and z = x+ iy e C. Calculate the following integrals on C = {z: |z| = 1}…

A: Cauchy integral formula

Q: dz where C:|z – 2| = 0.2 (z – 2)³(z – 5) by using (a) Cauchy's integral formula

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Q: 1- Assume that x, y E R and z = x + iy E C .Calculate the following integrals using the given…

A: Given :-  Assume that x,y ∈ℝ and z = x+iy ∈ℂ. To determine :-  The following contours :- (b)…

Q: Calculate the integral f. (z-2)²2 dz, where C: |z – 1| = 3.

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Q: Calculate the line integral of h (x, y) = (2xy) i+ (x² – 2ry) j; over r (1u1) = cos u i+ sin u j, u…

A: Here,hx,y=2xy i + x2-2xy jr(u)=cosu i+sinu j

Q: 1. Evaluate the line integral of E-xa, -y a, along the segment P; to P; of the circular path as…

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Q: Is dz

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Q: , (xy + 2)dV, 27. Calculate where B = {0 < x < 2, 0 <ys1, 1< z < 3} as an iterated integral in two…

A: Consider the following integral: ∫∫∫Bxy+zdVB=0≤x≤2, 0≤y≤1, 1≤z≤3 Consider the first way:…

Q: Evaluate the double integral S S (ax cos(y) + by + 1) dæ dy where R: |r|+ |y| < 6. O 1+a 72 O o O…

A: Use odd and even function integral.

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: y 3 2-…

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Q: 1. Evaluate the given line integral, |(-y,x – y) · dR, where C is the upper part of x² + y? = 1 from…

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Q: 1- Assume that x, y E R and z = x + iy E C .Calculate the following integrals using the given…

A: Note: According to our guidelines We’ll answer the 3 subparts of the question since the exact one…

Q: Calculate the integral f. dz, where C: |z| = 1. (2z+1)(2-2)

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Q: 1- Assume that x, y ER and z = x + iy E C. Calculate the following integrals on C = {z:|z| = 1}…

A: Use cauchy theorem for complex integral.

Q: 1-) Assume that x, y E R and z = x + iy e C and answer the followings. Calculate the reel integrals…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: У 3…

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Q: 1- Assume that x, y € R and z = x + iy € C .Calculate the following integrals using the given…

A: a) Given ∫0∞lnx1+x2dx ∫0∞lnx1+x2dx=12∫-∞∞lnx x-ix+idx=122πi Resi=πiln i2i=π2ln i=π2ln1+π2 i=π20+π2…

Q: (b) Evaluate the following integrals: z²+cosz (i) [ezsiniz) + + sin22]dz, C: |z| = counterclockwise.…

A: (i) Given integral is∮Cezsinz+z2+coszz10+sin2zz2dzC: z=π2 counterclockwise.The integral is evaluated…

Q: Calculate the double integral of f(x, y) over the triangle in the figure below. f(x, y) = 6ex 4 3. 1…

A: According to the given information, it is required to calculate the double integral of f(x,y) over…

Q: Set up a double integral to find the z = x? + y? %3! %3D z = 0

A: We are asked  to set up double integral to find the volume.

Q: Evaluate the line integralſ (x + 2y) dx + x² dy, where C consists of line segments from (0,0) to (2,…

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Q: Calculate the line integral of h (x, y) = (2xy) i + (x² – 2xy) j; over r (u) = cos u i+ sin u j, u e…

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Q: 3 7z Set up the iterated double integral S S g(x,y) dy dx as dxdy such that: (iki katlı integrali

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Q: Evaluate the line integralſ (x+2y) dx + x² dy, where C consists of line segment from (0, 0) to (2,…

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Q: Calculate the line integral of h (x, y) = (2xy) i + (x– 2ry) j; over r (u) = cos u i+ sin u j, u E…

A: Given function is  hx,y=2xyi+x2−2xyj To compute the line integral over ru=cosui+sinuj from 0 to 2?.

Q: 4. Compute cach of the following iterated integrals by reversing the order of integration. sin (r)…

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Q: Find the integral f(r, 0) = 4r², where 1 <r< 3, -T < e <n of

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Q: Calculate the double integral of f(r, y) over the triangle indicated in the following figure: 4 3…

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Q: 1- Assume that x, y ER and z = x + iy E C. Calculate the following integrals on C = {z: |z| = 1}…

A: By residue formula we can solve the problem

Q: Evaluate the following line integral I=[3x°dx + 2yzdy +y°dz from A: (0, 0, 0) to B: (2, 4, 8) a) By…

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following fhgure y 4 3…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Compute the line integral of f = x? - y, along C:x² + y? = 4 in the first quadrant from (0,0) to…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate the iterates integrals 2) r*dA D = {(x, y) : 1 < a <e, 0< y S In(x)}

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Q: 1- Assume that x, y ER and z = x+ iy € C. Calculate the following integrals on C = {z:|z| = 1}…

A: We have to evaluate  ∮C1z2−iz+34dz on C=z:z=1 Here, fz=1z2−iz+34…

Q: 2- Assume that x, y e R and z = x + iy E C and answer the followings. Calculate the reel integrals…

A: Consider the given figure in the question. We have to evaluate I=∫x=0∞1x3+1dx in the given contour…