4. Find the value of the integral 223 + 5 'zp- c (z – 1)(2² + 9)* taken counterclockwise around the circle (a) |z – 2| = 2; (b) |2| = 4.

Q: 5. Verify Green's Theorem for 0(xy +x )dx+(4x-1) dy where Cis shown below by (a) computing the line…

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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – 1 dy y? dr+ (1,2) Moreover…

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Q: 1. Calculate the integral 1 y-stnx)dx + cosy dy a) With directly (classical), b) With the Green's…

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

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A: Given:

Q: Q0 Integrate 2 from x? o to L x²_2 trapezaidal rule with four

A: SolutionIntegrate x2-2 from 0 to 4using the trapezoidal rule with 4 bandsFormula of trapezoidal…

Q: 1. What should be A for the path independent of (2,4) xy + A 2dy – x y? fip- (1,2) Moreover evaluate…

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Q: AIS. 4. Compute the area of the surface formed when f(r) = 2 + cosh(r) between 0 and i is rotated…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Verify Green's Theorem by evaluating both integrals √ y² dx + x² dy = √ √ ( Ox (ON-OM) c for the…

A: Here we have to verify the Green's theorem.

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0). (2,2) and…

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Q: Evaluate the integral (2x – y) dx + (x + 3y) dy along the path C. C: x-axis from (0, 0) to (0, -3)…

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Q: Evaluate the line integral along the given paths. | xy ds (a) C: line segment from (0, 0) to (5, 4)…

A: We need to evaluate,                          . For (a), .

Q: The approximation of the integral -2) In (x+2)dr using the two points Gaussian quadrature மாmua is)

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Q: Suppose that (z, y) = e-v and o(In 2, In 2) = 1. Please use the technique of %3D linear…

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Q: 1. What should be A for the path independent of (2,4) xy + X -dx + 2Ay – x -dy. y? Y (1,2) Moreover…

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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: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: 16. Let D-((, y, z):05zs2, 0≤ y ≤1, 05:5z+y). Find the triple integral: 72xy³ dv.

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Q: 2 1 To evaluate the improper integral . v3+ 125 will tend to infinity). What is the minimum value of…

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Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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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: 3. Compute the line integral of F(x, y) consisting of the line segment from (T,0) to (2, 5),…

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Q: Evaluate the line integral ſ. 8y² dx + z² dy + (100 – x²) dz over the quarter of the circle of…

A: To evaluate the below line integral. ∫c8y2dx+z2dy+100−x2dz Here c is the quarter of a circle of…

Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

Q: 9. Evaluate the integral ex V2e-2x – 3e2x 2/2e-2x – 3e2x +C А. 1 3eªx – 2+C B. 2/3 Arcan V3e2x…

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Q: 3(e). If it is true that the line integral F. dr 0 for all closed curves C₁ show that the line…

A: Given: 3C.For all closed curves C, line integral ∮CF.dr=0 and line intergral over a non-closed curve…

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where u> |z| > 0

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0<z<π…

Q: 3) Show that the line integral is independent of path and then evaluate the integral: S. sin y dx +…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: Consider the integral 2 6z² In(z) dz

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Q: 2. Evaluate O (2y + In(5x² +3)) dx + (10x 3) dy along the boundary of the elliptic- region 4. y? 1…

A: Introduction: Green's theorem is very efficient in calculating line integral. When the line intgeral…

Q: Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i +…

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Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

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Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: Integrate f(z) = 1 counterclockwise around the unit circle, using 28 – 4.4 Cauchy's integral theorem…

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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: 15. Evaluate the line integral J.(3xy* - 6xy ]dx + (4x°y³ - 3x?) dy, where C is any path from (1,2)…

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Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

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Q: rea bounded by the small loop of the limaçon r 1 2 sin e is given by finite integral

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Q: 11. Use Green's Thm to evaluate the line integral if the curve C consists of 3 line segments, from…

A: Solution:-

Q: 5, find the line integrals along the given path C. In 13. | (x – y) dx, where C: x = 1, y = 21 + 1,…

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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – x dy. y? -dx + (1,2) Moreover…

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Q: Set up the iterated double integral 9-9x SS dy dx of x 1. the limits . the limits of y

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Q: Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy], where C is the closed curve that…

A: The region of integration C is divided into three line segments C1, C2 and C3. Let C1:y=0,…

Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

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Q: 2. We have seen that the FTC for line integrals implies fc Vf - dĩ = 0 for any smooth closed path C…

A: FTC for line integrals implies ∫C∇f·dr→=0 for any smooth closed path C and any smooth function f (a)…

Q: Use the calculus of residues to evaluate the improper integral COSX -dx. (x²+1)³

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Q: - 322 - 4x - 5 Set up but do not evaluate the integral to find the length of the arc of the curve y…

A: Given query is to find the integral form arc length.