3. Calculate the following integrals over the given C curves by using the Cauchy integral formula. e-2 a) 6- dz C: Z- i| = 1 circle (z+ z3 dz (Z+2)2(Z-1) C: |Z + i| = 3 circle %3D

Q: Evaluate the integral fo F. dr for F = (2x²y)i + (3x² − 2xy²); on the curve C consisting of the…

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Q: 12 sin°(z) dr: C is any closed curve -dz enclosing 7/6 (a) Ic 6z – T -

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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: 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: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. | xy?…

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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: Let C be the curve represented by the equations x = 10t, y = t², (0 ≤ t ≤ 1). In each part, evaluate…

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Q: Evaluate the line integral, where C is the given plane curve. √ex dx, ex dx, C is the arc of the…

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

A: 2 Given integral is ∮Cezz+1z−2dz. a We have to evaluate the given integral if Cis the circle z=3.…

Q: Evaluate the integral [(e' - y)dx + (sin y +x)dy using Green's theorem where C is 16 bounded by y =…

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Q: For each of following equations find the general integral and compute three different solutions.…

A: We’ll answer the first question since the exact one wasn’tspecified. Please submit a new question…

Q: Let C be the curve represented by the equations X = 11t, y = t², (0 ≤ t ≤ 1). In each part, evaluate…

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Q: Evaluate the integral 1 = [ (10x y) dx + (y² + x²) dy where C is along the first quadrant of the…

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Q: Given gamma is the curve defined by R(t) = ti + tj + tk, for t [1, infinity). How would I evaluate…

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Q: where y is the circle {|z – 2| = 1} with counter clockwise orientation. (b) cos(2) -dz, 22 + 2iz – 1…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. [ (5y +…

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Q: Evaluate the integral (2x +3y)dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

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Q: SECTION B (60 marks) Candidates must attempt THREE questions being careful to number them B9 to B18.…

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Q: f(z* - y)dz – 2rdy where C It's the curve x? + y? = 4

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Q: Calculate the integral | (y? + 2?)dx + (2? + a² )dy + (x² + y²)dz where C is the curve intercepted…

A: C is the intersection of two surfaces : x-r2+y2=r2z2=2R-xx The coordinates will be :…

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

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Q: The graph shows the parabola c(z) = 11 - 2x², together with a shaded region. 13+ 12 11 10- 9 8 7 6-…

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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: (x² + y²)dx + 2xydy where C It's the curve y = x³ from x = 0 to x = 1

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Q: # 2. So sin 32 dz C: Izl=3 (z-5)

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