Q3) Calculate the following integrals over the given C curves by using the Cauchy integral formula. dz C: |zi| 1 circle a) - (2²+7²) z3 (z+2)²(z-1) b) - -dz C: |zi| 3 circle

Q: The length of the curve y = 3 - 4Vx for 0 < x < 3 is calculated by the integral: %3D Select one: 3 O…

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Q: -(1,2,3) What should m be for the integral S00 (2xyz? + 3)dx + (mx²z³ – 2)dy + (3x²yz² + 4z)dz to be…

A: The curl of a conservative field, F→ is 0→ . In that case, the line integral of F→ is path…

Q: 7. Find the area bounded by the parabolas x² - 4y = = using vertical strip. 0 0 and x² + 2y and x² +…

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Q: Calculate each integral, assuming all circles are positively oriented: dz, where y is the line…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: part öf the cicle42| = 2 in the first quadrant. Find an upper bound for the integral . b) Let C be…

A: Solution-(a) the path of integration has the length L=4π Upper bound M for the function =1z2+1;z=2…

Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

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Q: Without evaluating the integral, show that √ √ 2 ² 4+1 4₂ | 15 | 1/2 dz where C is the line segment…

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Q: Let F(x, y) = (3y, 2x + 2) and let C be the top half of the unit circle, beginning at (1,0) and…

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

Q: [[(2x + y²) da + 2xy dy], where C is the line segment from (-1,0) to (1, 2) Evaluate in two…

A: The line integral ∫CMdx+Ndy involves the integration over a specific path. In this case, the line…

Q: Calculate the line integral F. dr, where F (3y, -3z, 2x + 2) and C' is the boundary of a triangle…

A: We will find line integral by using stokes theorem .

Q: E Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [ 4³…

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Q: Evaluate the contour integral z²dz along the following curves. (a) C₁: the line segment from -i to…

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Q: 5. True or False? The work done by a force field F on an object moving along a path C is F. dr. (a)…

A: I am only providing the solution of question (5)   as there is no question (6) in the image.

Q: ²²-i)² dx 2³+dz when the contour C is the circle |z − 21 = 5 +4 1 Z- COSZ Cosz, dz when the contour…

A: According to the guidelines only three subparts should be answered. Therefore to answer the rest of…

Q: Qz/ Evaluate the complex integral: dz (z+ 1)(z – 2) where C is: a) The circle Iz] = 3 b) The circle…

A: Note:- If z =(x+i y)  then z =x2+y2 Cauchy's Residue Theorem:- ∮Cfz dz =2πi sum of residue   Given…

Q: = Jó 7xds where C consists of the arc C₁ of the parabola y 3x² from (0,0) to Compute the integral I…

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Q: The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal…

A: We have to solve given problem:

Q: Evaluate the integral (xy + xy²) dx + (2x² + x²y) dy over the curve C, defined by going in a…

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Q: Sc F. dr where F(x.y) = (3x² – 4v)i + (27 + cos(,³))j

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Q: Q4. a) Evaluate the following integral: 3 sin(5x? + 5y²) dA where Ris the region in the first…

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Q: 1)a) What is the area under the curve y = 2³ and above the x-axis between z = 1 and 2 = 3? What is…

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Q: Evaluate the following integrals: exp(inz) (a) Jc 222-522dz, where C is the circle |z| = 1 with…

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Q: 3. Find of 35 + 4 (5-2)(ャ)

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Q: A) Give f(x)-V-3 find f-*(x) ,x >0 B) : Find the area bounded by the curve y = f(x) =v2x +1 and the…

A: We have to find  A) f-1(x) for f(x) =√(x-3)  B) area bounded by the curve y = √(2x+1) and the lines…

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: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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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: 2z-3 3. Jc 3-372+4 dz, where C is the circle |z| = %3D counterclockwise.

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