Exercise 7. Let f(z)=4Re(z) and C be the line segment connecting 1+i to 0. Then the integral of f over C is equal to * O -2(1+i) 2(1+i) O 4(1-i) O None of these

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A: Explanation of the answer is as follows

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

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

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Q: 1. Evaluate the iterated integrals. In 3 In 2 (a) f f e** dydx S S 00 (b) ff X 00 (xy+1) dydx (c)…

A: This question is related to double integration, we will solve it using given information.

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A: From: (0, 0) to (5, 0)y=0, dy=0∫ y2 dx+ x2 dy =0From: (5,0) to (5, 9)x=5, dx=0∫09 x2 dy= ∫0925…

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

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Q: a) Let f(x) = 35 – 2a-1 +5+ 7x². Compute the integral of f. %3D

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Q: 1) э бирорце f a ad да ore integralbl on [a,b]. Show that of -g is also integralible салоз.

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Q: Compute the double integral of f(x,y) = 36x³y over the given shaded domain in the following Figure :…

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

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A: Solution:

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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)

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Q: (1) Evaluate the line integral of F (x, y) = (x – y, x²) over the line from (1,0) to (3, 2). |

A: evaluate line integral in following way

Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 a. dz S dz b. So 22(2-1)" z(z-2)4…

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Q: 60. Calculate the integral of f(x, y) = e3x=2y over the parallelogram in Figure 7. (6, 4) |(1, 3) D…

A: Consider the given integral, fx,y=e3x-2y consider the given parallelogram in the figure, the…

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Q: Evaluate the integrals in Exercises 23–26. TT 23. cos (x + y + z) dx dy dz 0 Jo Jo -In 7 cln2 cIn5…

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A: Given fx,y=18x5y

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A: To evaluate the integral: ∫3sin2tdt. We know that, sin2x=1-cos2x2 Therefore, using this formula,…

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Q: Evaluate the given line integral. | (y, -x) dR, where C consists of 4y = x² from (-2, 1) to (2, 1)…

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Q: Evaluate the iterated double integral. I 3 3y be dady A

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Q: 2- Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reel integrals…

A: a)The given integral is,  ∫0∞1x2+1dx

Q: 1. Express the integral S S f(x,y, z) dzdxdy as an iterated integral in the other five different…

A: I1=∫02∫0y3∫0y2f(x,y,z) dz dx dy0≤y≤20≤x≤y30≤z≤y2I2=∫08∫0x3∫0y2f(x,y,z) dz dy dxx=y3,y=x30≤y≤x3y=0…

Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 b. dz a. √21-23 = dz · Soz (²-2) 4…

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Q: Let f(z)=4Re(z) and C be the line segment connecting 1+i to 0. Then the integral of f over C is…

A: Given function is fx=4Rez and C be the line segment connecting 1+i to 0 We have to find the integral…

Q: Exercise 7. Let f(z) =4Re(z) and C be the line segment connecting 1+i to 0. Then the integral of f…

A: we have fz=4Rez Now, z=x+iy ⇒zt=xt+iytdz=dx+idy∴ dzdt=dxdt+idydt we have straight line y=x Let x=t,…

Q: Use the Substitution Formula in Theorem 7 to evaluate the integrals in Exercises 1-24. 2. а. rV x3…

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