Evaluate the following line integrals in the complex plane by direct integration (not using theorems) -1+i dz along the indicated path -1 1

Q: Evaluate the following integral in cylindrical coordinates. 2 14-x2 1 dz dy dx -2 0

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Q: Calculate this integral a Sat-x? 3/2 x²+y²)¯ dy dx -a

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Q: 3) Evaluate the iterated integral by converting. polar coordinates the to as to bo a) √x²+y² dy dx

A: Solution 3: a: Given  ∫01∫02x-x2x2+y2dydx Here 0≤x≤1 and y=0 to…

Q: 3) Evaluate the iterated integral by converting the to polar coordinates -√₂x-x² a) √²ty² dydx…

A: Given that, The integrated integral: (a) ∫02∫02x-x2x2+y2dydx,  such that , the region is…

Q: Calculate by u- Substitution, the follo wing integral definite 3 • cos x • sin x •dx

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Q: Calculate the iterated integral a) [ [ (6xy² – 2x) dy dæ

A: In this question we have to find Double Integration. First find in terms of y and then in terms of…

Q: From the basic definition of complex integration, evaluate the integral o f(z) dz, where C is the…

A: Let us parametrize C: the unit circle enclosing the origin by z=eit. Here, f(z)=z2. Now, we need to…

Q: Evaluate the integral de. f(0) = Lo sinh 0 – a %3D “ OP- where a is a complex number (Im a + 0.)

A: Given function is  f(θ)=∫-∞∞θsinhθ-adθ or we can write it as f(x)=∫-∞∞xsinhx-adx     (1) since…

Q: 1 dA 1+ 6y x [0, 1] sin(2x) R - %3D 4' 2 R

A: Given: ∬sin2x-11+6ydAR and R=π4,π2×0,1 To find: The value of integral.

Q: Evaluate the integral.  integral  t 2 sin 2  t dt

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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: Evaluate the integrals in Exercises using integration by parts. 3. f cos t dt 4. * sin x dx

A: The formula for an integral ∫udv is uv-∫vdu. Here u function is selected on basis of ILATE order.…

Q: Evaluate the iterated integral. * Tt/2 r cos 0 dr de dz -1Jo

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Q: Convert the integral to polar coordinates and evaluate. V49 - x2 sin(x2 + y2) dy dx V49- x2

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Q: The value of complex integral J zdz is č (z + 1)

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Q: Evaluate the integrals in Exercises 2. J 3 dx dx 1. 9 + x VI + 9x

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Q: 7/2 y3 cos os 2y dy

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Q: 1- Find the integral of: 2 cot - de T/2 A- B- / dr Vr

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Q: Integrate f(z) = (7)° counterclockwise around the unit circle, using Cauchy's integral theorem if…

A: using cauchy residue theorem to find given integral...

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 Riemann-Stieltjes integral cos(r) da(r) where a(x) = E 2-"I(x – n-1).

A: Given:Integral ∫02cos (x) dα (x)where α(x) = ∑n=1∞2-nI(x-n-1)

Q: Calculate the following integral counterclockwise around the curve C: |z| = 1. 1 cos z - dz Cos z e…

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Q: Show that for c =5 that PV sin r dr + PV | sin(x+c) dr. This shows us that when the improper…

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Q: Evaluate the integral (t³ In ti+ 3t³ sin (t) j+k) dt.

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Q: Evaluate the integrals in ∫7cos t sin t dt

A: Given Integral,I=∫7 cos t sin t dt

Q: Evaluate the integral. |a cos(6 z) dz =| %3D

A: Topic:- integration

Q: Estimate the double integral_R  (3xy^(2)+2x^(2)) dA where R= [0,1] x [0,1] by diving R into four…

A: We need to evaluate integral.

Q: Evaluate the integral by converting to polar coordinates. 2. V4-x2 cos(x + y) dy dx

A: To evaluate the given integral by transforming it into polar coordinates.

Q: Compute the integral COS I dx (x + a)2 + B2 where a E R and B> 0.

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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: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

Q: Evaluate the iterated integrals a. (x-y)dydx b. cos y dxdy

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Q: Calculate the following integrals using the Cauchy integra formulas. a) -dz, l2l=2 (2 – 1)²(z – 3) |…

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Q: Evaluate the iterated integral. TT/2 (10 cos(e) r dr de of

A: ∫0π2∫010cosθrdrdθLet∫010cosθrdr=[r22]010cosθ∫010cosθrdr=[(10cosθ)22-0]∫010cosθrdr=[100cos2θ2]Therefo…

Q: Calculate by using integration by substitution, Sec V11 tan15 da What was yoOur substitution? What…

A: Given that ∫sec2x11tan15x11dx find out the integral by substitution

Q: Evaluate the integral. cos(6 z) dz %3D

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Q: Evaluate the following integrals (taken anticlockwise) using Cauchy's theorem: (f) P.„(²+1)² eiz dz…

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Q: Evaluate the iterated triple integral f S Sesin(y) cos(0) dp dp de. Present the answer in exact form…

A: Evaluate the iterated triple integral ∫0π2∫02π3∫04ρ sinφ cosθ dρ dφ dθ

Q: w/2 x cos cos z dy dx dz

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Q: Find the integrals. a) R= %3D R.

A: First we have to plot region of integration.

Q: Use the Residue Theorem to evaluate the a? integral dx + x2 where a>0

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Q: Evaluate the Line Integral through the Path ab in the below Figure. for the F = p cos o a, + z sin o…

A: The general form of a vector valued function in cylindrical coordinates is given by F=F1aρ+F2aϕ+F3az…

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

A: the double integral formula  ∫x1x2∫y1y2f(x,y)dydx the value of y varies from 0 to 3 and the value of…

Q: The result of the integral in 0 given V Vr²- 25 -dy is 5 tan0 -50 +C, True B False

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Q: Determine the following integral in the complex plane. sin(z) z° - 3z* + 2z³ 3 where C is the circle…

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Q: Use the Fundamental Theorem to evaluate the definite integral exactly. 1 (16 + y® )dy Enter the…

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Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…

Q: and evaluate the Sketch integral reverse 9/x Jy dz

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