1-) Assume that x, y E R and z = x + iy e C and answer the followings. Calculate the reel integrals for a given countour in figure 1 .(Consider R → 0o, Cq € (-R, +R) ) Imfa} C2 x2 a- f-o 41 dx x=-0∞ x4+1 Re(z) -R R.

Q: Compute the double integral of (x – 2y) Væ + 2y o i over the quadrilateral with vertices (0, 0), (4,…

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Q: dx Evaluate the integral V1 + 9x² 1) Which substitution will change the integral into one of the…

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Q: e In (xle ) (2– sec²x) sec(3A – x) sec³x dr What should be the value of A for to be integrable using…

A: integration by substitution method

Q: 3 Evaluate the integral de using the two-point Gaussian quadrature rule O -|4 1035 N/N N/W 끔

A: We have to evaluate the integral ∫−3311+x4dx by using two-point Gaussian quadrature rule. Here,…

Q: Calculate the iterated integral A 67 5x cos y dydx. 1 2n 5

A: Explanation of the answer is as follows

Q: 22. Evaluate the iterated integral. (b) f. [, 2x + »)'dy (a) x+y+ xy dydx

A: Now we will solve the given double integral  We know integration of Xn dx = X(n+1) / (n+1) + C ,…

Q: Calculate the improper integral 2 x+y+ z" . e 2 2 2 -x-y -z 2 8. dxdydz.

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

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Q: 13. Evaluate the triple integral: In y (z) dzdydx y2

A: Given :∫12∫1x∫y2lnyz dz dy dx=I

Q: dz where C:|z – 2| = 0.2 (z – 2)³(z – 5) by using (a) Cauchy's integral formula

A:

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: 1- Assume that x, y E R and z = x + iy E C .Calculate the following integrals using the given…

A: Given :-  Assume that x,y ∈ℝ and z = x+iy ∈ℂ. To determine :-  The following contours :- (b)…

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3 1…

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Q: (a) Compute the multiple integrals of (i) V4-z2 1 xy dxdydz (11) SS, (8 – x² – y²)dA, where R = {(x,…

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Q: 1. Give iterated integrals for r (x² + yz)dV where E is in the first octant bounded by the planes: y…

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Q: Use Green's Theorem to evaluate the integral 3x²y²dx + (5y³ – x³y²)dy, C

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Q: I.Evaluate the ff. iterated integrals. • 7d/2 ptan y sec y 1. .3 cos' ydxdy JJ

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

Q: 5. Calculate the double integral f, 2x cos(xy) dA , R = [0,2] × [0, 7]

A: We need to compute the value of the double integral ∫02∫0π2xcos(xy)dydx. Since, this is simple…

Q: Suppose that (x, y) = x+ 4y on the domain D = {(r, y) | 15x< 2, x? sys4. D Then the double integral…

A: Given that, f(x, y) = x + 4y and   {1≤x≤2},  {x2 ≤y≤4} We have to calculate the value of ∬Df(x, y)…

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

A: Cauchy lemme

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3…

A:

Q: Suppose that f(r, y) = 2x + 4y at which {(x, y) |-1<a < 3, - 1<y< 3}. Then the double integral of…

A: ∫∫Df(x,y)dx dy=∫∫D2x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13x2+4xy3-1…

Q: 1- Assume that x, y E R and z = x + iy E C .Calculate the following integrals using the given…

A: Note: According to our guidelines We’ll answer the 3 subparts of the question since the exact one…

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

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Q: 2. Evaluate the improper integrals of (a) In r dr OP -2 (0 + 1)³/5 (c) / re dr 4 dr (4) L r² + 16

A: To find - Evaluate the improper integral of    Formula used - Integration by parts :

Q: 4 Evaluate the indefinite integral by using the substitution u = y² + 4y² + 2 to reduce the integral…

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Q: 2. Evaluate. the fallowing.integrals.a.fter.seveoiag.the areler.of.integratiam. dydx Ans..In)/4 C.…

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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: The value of the improper integral / 36 z² e ² dz = 12e1 O - 36e 1 O 36e 1 O 12e 1

A: We need to evaluate the value of the following integral I = ∫1∞36x2e-x3dx

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: 9. In evaluating the improper integral dx , which of the following is true? (1– 3x)2 3 (A lim 3x 1…

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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…

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: Evaluate the double integral. 8xy2 dA,    D is enclosed by x = 0 and x = (4-y^2)^1/2

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Q: 2_ Calculate the generalized integral. x In r dx J. (1+12)3

A: The given integral: Calculate the above integral:

Q: Evaluate the iterated integral. In 3 In 4 e 4x +y dy dx 0. 1.

A:

Q: Compute the double integral of f(x, y) = 18xy over the given shaded domain in the following Figure :…

A: Given fx,y=18x5y

Q: Suppose that f(x, y) = e² / Y on the domain D = {(x, y) | 0 < y < 2,0 < x < y³}. D Then the double…

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Q: Apply the techniques of Example 7.1.5 to the evaluation of the improper integral 8 dx 1 = (a) Let…

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Q: 7. Verify Green's Theorem for O (6+ x²) dx + (1 – 2xy) dy where C' is shown below by (a) computing…

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Q: Set up the iterated (triple) integral for the integral ]]] xy¹z³ dV where S is the tetra- S hedron…

A: We will find limits of variable and then find value of integral

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

A:

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: Evaluate the iterated integral. 6. 7 8 (x² + y² + z² ) dx dy dz -6 0 0 6 7 8 (x² + y² + z² )dx dy dz…

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Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

A: We have to find value of given triple Integral.

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: Evaluate the integrals in Exercises 9–12. 4 cos (x²) dx dy 2y 9. e dx dy y/2 10. 27 sin 7x² -dx dy…

A: Given: