(b) Find the value of the following integrals: z-1 1- (z'+z-2)" z = 3i, z 2. dz, y is the triangle with vertices at the points z =-51,

Q: 4) Evaluate the following integrals: a) SII (z² + + 1)ev² dx dz dy . R = [0.y] × [0.20] × [0. In 0]

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…

Q: 6.4.12 Please help me solve these math practice questions.

A: Area of the curve y= cos(4x)  Where -π/8<x<π/8

Q: Evaluate the following integral in cylindrical coordinates. 5 12 14-x2 -x-° dy dx dz 0 0 x

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Q: 8) By using the double integral in polar coordinate, find ,"[S" e-x²+y>dx]dy

A: The double integral in polar coordinates is given by the formula ∬Rf(x,y)dxdy= ∫ab∫g(θ)h(θ)f(rcosθ,…

Q: 5. Calculate the double integral f, sin(2x) cos(3y) dA , R = [0, 1/2] x [0, 1]

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Q: Consider the triple integral: (ʃ_2^3 ʃ_4^8 ʃ_0^10 sin(xy-z) dxdydz).  Use a change of variables to…

A: To evaluate: ∫22∫48∫010sinxy-z dx dy dz by change of variables Consider the transformation…

Q: 3 2(x²+1)7 Write down an integral that gives the ARCLENGTH of y on the interval from x = 0 to x = 2…

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Q: T 3. fz sin4 y cos7 y dy 2

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Q: 6. Evaluate the line integral (x? + y² )dx – x dy along the curve C: x? + y² =' counterclockwise…

A: Given: ∫c x2+y2 dx- x dy  We have to Evaluate the given line integral along the curve C: x2+y2=1…

Q: Sketch the domains of integration of the double integrals (a) Laxf dx xydy √(1+y) 0 R/2 (b) dy (cos…

A: Here, we need to sketch the domains of integration.

Q: Calculate the integral (x – y) dx + (x + y) dy I = x2 + y2 where L is along the curve y = cos x,…

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Q: Evaluate the line integral by the two following methods. xy dx + x?y3 dy Cis counterclockwise around…

A:

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: Evaluate the integral / cos[3 +1/(z – 3)] dz, where Y is the unit square with corners at 0, 1, 1+i e…

A: Given; ∫γcos3+1z-3dz Where, γ is the unit square with corners at 0,1,1+i e i

Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: 1. Prove that L{cos(at)} cos(at)dt integrating by parts twice and the evaluation of the improper…

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Q: 4. If the curve y = In x between x = 1 and x = e is rotated about the y axis, which integral below…

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Q: Calculate the double integral. 9x sin(k + y) dA, R = 0, 풍핑x [o, 플]

A: First we will evaluate the inner integral wrt 'y' and then evaluate wrt 'x'.

Q: 8. Depending on the real parameter p and q, what can you say about the result of the following im-…

A:

Q: Calculate the iterated integral. 1/2 (y + y2 cos(x)) dx dy

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Q: Calculate the following integrals. In both cases the curve C has a counterclockwise direc- tion: 4.1…

A: We will find the integral by using Cauchy Residue theorem:

Q: Evaluate the following line integrals in the complex plane by direct integration (not using…

A: Complex

Q: (1,0) (1,0) 1 = | (x² – y²) dx – 2 x y dy + i - 2 x y dx + (x² – y²) dy (0,1) (0,1) Calculate the…

A:

Q: 4. the value of the given integrals | z - i | = 2,(z € C) around the circle compute for positive…

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Q: Evaluate the double integral I. y sin(a* )dA R where Ris the triangular region with the three…

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Q: Evaluate the double integral y sin(2³)dA where R is the triangular region with the three vertices…

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Q: 9-x2 C: Change to polar and evaluate the double integrals S (x3 + xy?)dydx V9-x2

A:

Q: (b) Evaluate the following integrals: z²+cosz (i) [ezsiniz) + + sin22]dz, C: |z| = counterclockwise.…

A: (i) Given integral is∮Cezsinz+z2+coszz10+sin2zz2dzC: z=π2 counterclockwise.The integral is evaluated…

Q: y? = 1? Which of the following integrals represents the length of the upper half of the ellipse 25…

A: Topic = Application of integration  Correct answer = A

Q: Find the value of 1-1/16 (x² + y²) dy dx + ſ', [~ ² * (x² + y²) dy de by expressing it as one…

A: From, the given integral, draw the region of integration.

Q: 1. Evaluate the integrals and sketch the region of integration. 1) º, S(+y +1)dædy 2) So , 1 sin…

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Q: 13. compute the integral // e10(x-y)²+8zy dædy over the ellipse & := {(x, y) ; 5x² + 5y² < 6xy+ 1}.…

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Q: 10. Use a definite integral to find the exact area enclosed by the x-axis and the parametric curve =…

A: The given parametric curve is: x=2t3+1    and     y=2t-t2

Q: Find the value of the closed loop integral z3 + sin z -dz (z – i)3 taken around the boundary of the…

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Q: 11-y² x 26)A) Convert the integral J Jax?+ y²)dzdxdy to an equivalent integral in -1 0 0

A:

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: 16–x² Choose the iterated integral that is equivalent to y dy dx in polar coordinates.

A: let x=rcosθ and y=rsinθ dydx=rdrdθydydx=r2sinθdrdθ 16-x2=yx2+y2=42=r2 r=4 Therefore r varies from 0…

Q: 18. Along the curve r(t) = (cos t)i + (sin t)j – (cos t)k, 0 < t < m, evaluate each of the following…

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Q: Calculate the iterated integral.   Integral_-8^8integral_0^pi/2 (y + y2 cos(x)) dx dy

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Q: c) Evaluate the integral e* (x + 1) - dx, VI – x² using 3-points Gaussian quadrature.

A:

Q: to polar coordinates turns into an integral S S" x² + y² dxdy When converting the integral

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Q: ∲c ezt / (z2(z - πi))3 dz, with C : |z - 3i| = 1.

A:

Q: 6. By using the double integral in polar coordinate, find ff e-(x²+y')dA for the region enclosed by…

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Q: 2. Approximate the following integrals using Gaussian quadrature with n = 1 and n = 2. 1 1 2 -dx 4…

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

Q: Depending on the real parameter p and q, what can you say about the result of the following im-…

A: a ∫1+∞1xpdx=limt→+∞ ∫1t1xpdx     =limt→+∞ x1-p1-p1t   =11-p limt→+∞ t1-p-1   =11-p∞  =∞

Q: 19. Convert the integral S(x2 + y?)dz dx dy in cylindrical coordinates. Do not evaluate the…

A: Recall: To convert from rectangular to cylindrical coordinate :       Put       x=r cosθ      y=r…

Q: Use symmetry to evaluate the double integral. 10 sin(x) dA, R = [0, 2n] × [0, 21]

A: Integral

Q: Evaluate the iterated integral. Triple Integral: (Outside to inside) Integral from 1 to 7, Integral…

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Q: Evaluate the integral: L x2 + y² dy dx by using polar coordinates.

A: