5, find the line integrals along the given path C. In 13. | (x – y) dx, where C: x = 1, y = 21 + 1, for 0 < t < 3 14. dy, where C: x = t, y = t², for 1 < t < 2

Q: Verify Green's Theorem by evaluating both integrals Lv² dx + x² dy dA ax ay for the given path. C:…

A:

Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – 1 dy y? dr+ (1,2) Moreover…

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Q: 2. Evaluate each of the following line integrals in two ways∗ . (a) Z C1 F~ 1 · d~r, where F~ 1(x,…

A: Given vector field is F→(x,y)=(2x-cosy)i^+(xsiny)j^F→.dr→=(2x-cosy)dx+(xsiny)dy C1 is the…

Q: Evaluate the integral S (t³ In t ì + 3t³ sin (t*) j + x-2 *(x+1) k) dt.

A: We will use the fact that when we calculate the integral of a vector valued function we integrate…

Q: The particular Integral for (D² + 19²)y = sin19z is Yp 38 O Yp 19 O None O Yp Zacon19z 38

A:

Q: Evaluate the integral S (t³ In ti + 3t³ sin (t*) j+ x-2 X(x+1) k) dt.

A: In this question, we have to find the integral of the given vector function. Here we integrate the…

Q: 1. What should be A for the path independent of (2,4) 2Ay – x dy y? XY + A dx+ (1,2) Moreover…

A: Consider the given integral

Q: Suppose that (z, y) = e-v and o(In 2, In 2) = 1. Please use the technique of %3D linear…

A:

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: In 11 In y ex+y dx dy. Evaluate the integral 1 0

A: Find your answer below

Q: 1. What should be A for the path independent of (2,4) xy + X -dx + 2Ay – x -dy. y? Y (1,2) Moreover…

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Q: 1 10-10z Set up the iterated double integral f S S dy dr as dxdy such that

A:

Q: 38. Evaluate the integral dy + x³ dx for any closed path C.

A:

Q: dx 1 = [- 1+vx+1

A: To evaluate: I=∫dx1+x+1

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.

Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

Q: Aşağıdakilerden hangisi (arctan(ok*) 1+e2kx 2dx integralinin sonucudur ? A)…

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Q: Evaluate the integral S (t³ In ti+ 3t sin (t*) j+ ) dt. 1-2 x1)

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Q: -In 10 10 1 7. Sketch the region of integration dy dx In y and evaluate the integral.

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Q: In 31 In y Evaluate the integral ex+y dx dy. 1

A: I am attaching image so that you understand each and every step.

Q: 6. At time t, a particle moving in the xy – plane is at position (x(t), y(t)) where the x(t)and y(t)…

A:

Q: 1. Evaluate the following integrals: SS (6yz - 2y' kixdy, s = [1,4] × [0,3] a. 1 b. ||| sin 2x dxdy,…

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Q: The particular Integral of Dy = -5 is Yp = 00 Yp = 0 Yp = -5x O None of the choices Yp 2

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Q: If ulr. 0) satisfies V'u = 0 inr<1, u(1, 0) = S(e). show that Poisson's integral formula in R' takes…

A: Given, ur,θ=0 satisfies ∇2u=0 in r&lt;1. Also u(1,θ)=fθ To show ur,θ=1-r22π∫-ππfϕ1-2rcos(θ-ϕ)+r2dϕ…

Q: In 17 In y |ex+y dx dy. Evaluate the integral 1 0

A:

Q: 3. Show that for p> 1 and r E (0, 1), the integral below converge: dt tp

A: by limit convergence test we cab prove this, we have to treat the definite integral as summation…

Q: 15. Evaluate the line integral J. (3x²y* - 6xy ]dx + (4x²y³ - 3x°) dv, where C is any path from…

A: My=Nx means F is conservative vector field

Q: х-2 Evaluate the integral S (t3 In ti+ 3t3 sin (t*) j+ k) dt. x(x+1)

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Q: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: In z 25 If the triple integral So" Sõ So™² (xe¯y) dydx dz Find the upper limit value E.

A:

Q: Verify Green's Theorem by evaluating both integrals ам | y2 dx + x2 dy dA ду for the given path. C:…

A: Solution is given below:

Q: 1. What should be for the path independent of (2,4) 2Ay – x dp. y? xy + A dx + (1,2) Moreover…

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Q: 3 7z Set up the iterated double integral S S g(x,y) dy dx as dxdy such that: (iki katlı integrali

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Q: 15. Evaluate the line integral J.(3xy* - 6xy ]dx + (4x°y³ - 3x?) dy, where C is any path from (1,2)…

A:

Q: 4. Find path integral J xdx+ ydy, if L is the segment: x-1,y= and re (0.1]

A: Given x=t, y=t2, t∈0,1

Q: 11. Use Green's Thm to evaluate the line integral if the curve C consists of 3 line segments, from…

A: Solution:-

Q: is Theorem 1.6. The line integrals of f in D are independent of path if and only if f has an…

A: Given: The line integrals of f in D are independent of the path if and only if f has an…

Q: Evaluate the integrals et + 2e²' – e' dt e' dt 39. 40. e21 + 3e' + 2 e21 + 1 cos ydy sin? y + sin y…

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

Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy dA ax ду for the given path. C:…

A: This question is related to vector calculus solved in step 2.

Q: (1) Show that F(x, y) : (2x + y, x - y) is path independent and use the fundamental = theorem of…

A:

Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x du -dp y? dx + (1,2) Moreover…

A:

Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – x dy. y? -dx + (1,2) Moreover…

A:

Q: Suppose w = In(æ² + y² + z²) , Compute dw/du and dw/dv in two different ways: ue3" sin(9v) , y :…

A: GIvenw=ln(x2+y2+z2) where x=ue3vsin(9v) , y=ue3vcos9v and z=ue3vTo find∂w∂u and ∂w∂v

Q: Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy], where C is the closed curve that…

A: The region of integration C is divided into three line segments C1, C2 and C3. Let C1:y=0,…

Q: Compute the following Cauchy principal value integral: dx р.v. x4 – 1 п/2 -T/2 Зп /2 -27

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Q: 2 1 Evaluate the iterated integral S 18*y°dy dx. -2 0

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

A: