3.1 Use the Cauchy integral formulas to evaluate the eiz cos z -dz, Ie z2(2z – 37) | where C is the region covered by circle |z – 2| = 3.

Q: 5. Use the binomial expansion and Cauchy's Integral Theorem to evaluate P ( C=10 2n dz where C is…

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Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z *zp- Se z?(2z – 37) where C is the…

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Q: Calculate the following line integral: Jc Y dx – x dy Over the four curves C given by the following…

A: Note: According to the guidelines only one question will be answered at once please upload other…

Q: 1. Use Green's theorem in order to compute the line integral $ (3cos + 6y?) dx + (sin(5") + 16x³) dy…

A: Here the given integral is                               ∮C3cosx+6y2dx + sin5y+16x3dy

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A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1 The…

Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z -dz, La 22(2z – 37) where C is the…

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Q: 42. Show that the graph of d ae""cos wi is bounded by y = ae-ct and y = -ae-ct for a > 0 and c> 0.

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Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z dz, L.7(2z – 37) where C is the…

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Q: And the Vorume of the solid gererated by rovolung the reglon boundid by the given ines't (urves…

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Q: 12.If Ar is the area of a region R given by the integral AR drdy con a > 0 -3a J0 + =phip" The…

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Q: The particular integral of (De +1)y= cosx is O None of the choices zsinz 2 ICOSI 2 ECOSI 2 O zsinz 2

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Q: Find the area of the given reptunanalytically l.The inner loop of roZ +4 Cos &

A: r=2+4cosθTo Find: Area of the inner loop of the given region.

Q: This problem extends Example 5.14 and Exercise 5.19, allowing us to compute the following integrals…

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Q: 3. Set up the integral to find fSfr r dV where T is the tetrahedron in the first octant under the…

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Q: 3.1 Use the Cauchy integral formulas to evaluate the eiz cos z dz, Le 2(2z – 37) where C is the…

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

Q: х cos 4x dx; и 3D х, dv cos 4x dx =

A: Given that  u = x ;  dv = cos 4x dx and we have to integrate by parts the given integral that is ∫x…

Q: 5. Find the following path integral. C is one-eighth of a circle as shown. J x dx (Here Q(x, y) 0…

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Q: 1. The integral of J, \z|dz along any closed path y is 0.

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Q: Calculate the volue of the de integral 23 - 1 2 F soro fallowing c a) Cil2+1|= 1 Curves. 6)…

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Q: 3.1 Use the Cauchy integral formulas to evaluate the e cos z I. 7(2: – 3m) where C is the region…

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Q: 3. Compute each of the following integrals cosh z dz where C is the circle |2| = 2 2 In 2 – z sin 2z…

A: ∮cosh z(2ln2-z)dz where c:|z|=2=∮f(z) dz where f(z)=cosh z(2ln2-z)Now, f(z) has singularity at z=2ln…

Q: 1 Use the Cauchy integral formulas to evaluate the e cos z *zp- 22(2: - 37) where C is the region…

A: Given: Let  I =∮C  eiz cos zz2 2z-3π dz  .....1 And,  C is the region covered by circle z-2=3.

Q: Evaluate the following integral: JIS [xlnytan z dV if S = {(x, y, z) € R³ : − 1 ≤ x ≤ 0, e ≤ y ≤ 2e,…

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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: 2. Set up an integral to find the exact length of the curve defined by 1 f(r) 1 In r %3D where 1<r <…

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Q: Evaluate the integral S CO|CT CT | CO CT /Co NIC 8 dx using the two-point Gaussian quadrature rule.…

A: We have to evaluate the integral ∫−22816+x4dx using the two-point Gaussian quadrature rule. Here,…

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Q: Find the domain and limit ast approaches infinity of T(t): i+ [2e ]j+[arctan(t)] k 3 In %3D 7.

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

A: Given: (a) ∫-∞∞ x2x4+1 dx (b) ∫-∞∞ x2(x2+1)2 dx We have to calculate the (a) and (b)

Q: 9. Evaluate the integral = R from z₁ = 1 to Z2 = -1. where C is the above half of the circle

A: Given is the integral ∫Cdzz¯. where C upper semicircle. |z|=R, z1=1 to z2=-1

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Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: 3 For questions 8 and 3. consider the line integral Sx²ydx+xydy 1439) Evaluate the integral, if C rs…

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Q: 2. Show that, in the region D: 0 < x<1, 0 <y< x², the following double integral 1 dA =- In(2) x5 + 1…

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Q: 2. Use partial fractions to evaluate the following integrals f. f (z) dz, where C is the unit circle…

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Q: 3. Evaluate the following integrals, using the residue theorem. (a) f. sin z dz (e) £ 1 dz (c) dz…

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Q: Consider the 2nd order PDE -3u +6xu-3u w=cos(x). XX ху yy (a Determine the regions in the xy-plane…

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Q: This problem extends Example 5.14 and Exercise 5.19, allowing us to compute the following integrals…

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Q: Verify Green's Theorem by evaluating both integrals ƏN [_y² dx + x² ay = [] (ax - 3+²) da d'A dy ay…

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Q: 37. Evaluate the integral fи 4x³y dx + x* dy for any closed path C.

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Q: determine the area inside of the inner loop of the limaçon r = 2 cos 0 – 1.

A: We have to find area of r= 2cos(theta)-1