4. (45pt) Compute the following contour integrals and give reasoning. 2z dz (a) Jc 7(z+4) where C is the positively oriented circle of radius 3, |z| = 3.

Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-1,…

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Q: af 11. Suppose + = 0, prove that the line integral | F. fe -dx + ду dr = -dy is inde- pendent of…

A: Here F = fy i+fxj

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

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Q: Calculate the following line integral where C is the straight line from (1,2) to (4,7). S xy ds C

A: The given integral is I=∫Cxy4 ds where C is the straight line from (1,2) to (4,7). We have to find…

Q: Set up, but do not evaluate the integral for the length of the curve.

A: We know that length of curve y=f(x) from x=a to x=b is given by

Q: . Set up an integral to find the exact length of the curve defined by 1 fie) = - 1 In r 2 4' where 1…

A: Given curve is: f(x)=x24-ln x2,  1≤x≤2

Q: Evaluate the line integral y = x² from (-1, 1) to (1, 1) and the line segment from (1, 1) to (−1,…

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Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: Set up the line integral ∫c x2z ds, where c is the line segment from (1, 6, -1) to (- 4, 1, 5). (No…

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Q: 1. Let C be a path along the upper half of a circle from the point P(2,0) to the point Q(-2,0).…

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Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: | Use the Cauchy integral formulas to evaluate the eiz COS Z -dz, 2²(2z – 37)* where C is the region…

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Q: 3.2. Prove directly from the definition of Itô integrals that t t | B?dB, = B - | B,ds .

A: The answer is given below

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: Evaluate the line integral, where C is the given curve.     C xeyz ds, C is the line…

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Q: Evaluate the line integral xyld x + (x²+y)dy] +. where c is the saruare farmed by the lines

A: Let us consider a line integral ∫CP dx+Qdy then it can be written as  ∫D∫∂Q∂x-∂P∂y dA  Where, P and…

Q: Use the Cauchy integral formulas to evaluate the  ∮c eizcos z/ z2(2z -3π) dz,  where C is the region…

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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 given in the figure below

A: Given question is belongs to the vector calculus and from the line integration we have to integrate…

Q: Set up and evaluate an integral that represent the length of the curve. x=r-r', y=p",15 4 3/2 3 4.

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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: Use the Fundamental Theorem of Line Integrals to calculate d exactly. 7-7+4y²f arqund the top of the…

A: Given

Q: Find the integral ∮F • dR around the circumference of the circle x2 - 2x + y2 = 2, z = 1, where F =…

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Q: 2. Evaluate fy³ dx-r³ dy, where C is the circle of radius 2 centered at the origin, in the following…

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Q: Evaluate the integral, if C is the circular path y = (1-x^2) from (1,0) to (0,1).

A: Let y=1-x2 be circular path from (1,0) to (0,1). Parameterize the above path by taking x=cosθ , then…

Q: If C is the line segment from (6,3) to, (0,0), find the value of the line integral: Se(by? i+ 3z) -…

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Q: Evaluate the line integral Jo 9x²yzds with respect to s along the с 2 curve C: x=t, y = t², z = /t³…

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Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dĩ (6) where C is the…

A: (6) 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 ∫Cxdy−ydx along the curve C defined by the equation y=x3 from the origin…

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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: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

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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: 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: 2. Find the value of the integral of g(z) around the circle |z- il = 2 in the positive sense when 1…

A: Cauchy integral formulae: Let us define function f: D→ℂ and a∈D and 'C' is any closed curve around…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 7y3 dx…

A: See attached file for a step by step explanation to evaluate the given line integral.

Q: Calculate the following double integral as the inside of the circle R: x² + y² = 1.

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Q: Find the integral ∬Rydydx, where R is bounded by the straight line y=2x and parabola y=3−x2.

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Q: dz ; C is a circle Iz-1| = 1/2 z4-1 z2

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Q: 2) Let C denote the positively oriented boundary of the square whose sides lie along the lines x =…

A: Given line x=-2,2 &y=-2,2 is can be  solve as follow

Q: Without evaluating the integral, show that z+4 67 -dz s 7. 2i +1 IC where C is the arc of the circle…

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Q: 3. Evaluate the integral o f(z) dz, where C is the unit circle enclosing the ori- gin, and f(z) = 1+…

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Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.

A: Write the equation of circle into standard form. The radius of the circle is 1.

Q: O Evaluate the line integral over The Cur ve C. SCx+y+2)dx +6x +y-2)dy+ (x-y+2)dz where c is the…

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Q: If the curve y= from (0, 0) to (3,9) is rotated about the x-axis, the integral that represents the…

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Q: Use the Cauchy integral formulas to evaluate the eiz cos z dz, Yo z2(2z – 37) | where C is the…

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