.2 Evaluate the line integral xy dx + x-dy, where C is the path going counterclockwise around the boundary of the rectangle with corners (0,0),(2,0),(2,3), and (0,3). You can evaluate directly or use Green's theorem. Write the integral(s), but do not evaluate.

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

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Q: Evaluate the line integral 2 Cx2y)dx- 2xdy along each of the following closed paths, taken…

A: Given that the integral,

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

A:

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: find the line integrals along the given path C. ∫C (x - y) dx, where C: x = t, y = 2t + 1, for 0≤ t≤…

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Q: Find the line integral ye-xz ds Here, C is the path r(t) = [t,3t,-6t], 0sts In(8) ·

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Q: 5. Evaluate the integral xdx+ (x+y)dy where C is the curve x 1+y from (2,1) to (2,-1).

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

A: In this question we can verify the Green's Theorem . i.e, ∫C M dx +Ndy = ∫∫R ∂N∂x-∂M∂ydA .

Q: 10. Evaluate the integral cz(z-1) where C is a simple closed curve in the positive direction that…

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Q: Suppose F(x, y) = (6x + 5y)i + (5x + 4y)j. Evaluate the line integral for each of the given paths,…

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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: 7. Evaluate the line integral by using Green's Theorem feve'dx +2e*dy C is the rectangle with…

A: Green's Theorem, ∫CPdx+Qdy=∬D∂Q∂x-∂P∂ydA Compare ∫CPdx+Qdy=∫Cyexdx+2exdy Implies that, P=yex, Q =…

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

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

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Q: Evaluate the integral (6x-y)dx + (x+6y)dy along the path C, defined as y = 16-x² from (0, 4) (4, 0).…

A: Answer: The solution is given below:

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

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Q: Verify Green's Theorem by evaluating both integrals ax dA ду for the given path. C: rectangle with…

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…

Q: (b) Evaluate each of the following line integrals: (1) xds, where C is the portion of the curve x…

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Q: 1. Evaluate the given line integral, |(-y,x – y) · dR, where C is the upper part of x² + y? = 1 from…

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Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: 2. Evaluate the given line integral, (x – y, y) · dR, where C is the line segment from (0, 1) to…

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

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Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x – y)dy for the given path. C: x =…

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Q: 11 Calculatk the line integral , f (x,y)ds for the given junc rion and path xiyl=xy Ht)= for 0st<4…

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Q: By using Green's Theorem, evaluate the integral (1+xy') dx +x²y dy, where R is the closed R path…

A: From the given problem:   I=∫R1+xy2dx+x2ydy   From Green's theorem:   ∫F1dx+F2dy=∬∂F2∂x-∂F1∂ydxdy…

Q: Evaluate the line integral | H. dř; Ħ = e" î + [xe" + In(z)] ĵ + 22 k, and C is the path defined by

A: Given that  H→=eyi^+xey+lnzj^+2yzk^      (1)  and r→=t,1,1, t∈0,1                (2)      from…

Q: 2. Let C be the positively oriented boundary of the square whose sides lie along the lines r ±1 and…

A: According to cauchy’s integral formula for any region C,

Q: Evaluate the line integral H. dř; Ħ = e" ì + [æe" + In(z)] ĵ +2² k, and C is the path defined by 7…

A: Given H→=eyi^+xey+lnzj^+2yzk^ We know that dr→=dxi^+dyj^+dzk^…

Q: S. 09. (a) If A = (4xy-3x2z")i + (4y + 2x")j + (1 2x%z)k, prove that A• dr is independent of the…

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Q: Verify Green's Theorem by evaluating both integrals √< y² dx + x² dy = [] (ON - 3M) de dA ?х ду for…

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Q: 9. Evaluate the integral = R from z₁ = 1 to Z2 = -1. where C is the above half of the circle

A: Given is the integral ∫Cdzz¯. where C upper semicircle. |z|=R, z1=1 to z2=-1

Q: 4. Evaluate the integral f. x'y°dy – x5y'dx, where C is the square determined by the 0, y = 0, x =…

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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: Calculate the integral of f(x, y) = e*-2y over the parallelogram in Figure 7. y (6, 4) (1, 3) D (5,…

A: Let the given integral, f(x,y)=e3x−2y Now, from the figure of the parallelogram, let O(0,0), A(5,1),…

Q: 3 For questions 8 and 3. consider the line integral Sx²ydx+xydy 1439) Evaluate the integral, if C rs…

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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)…

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Q: 11 Calculate the line integral f Gy)ds for the given junc rion and path xiyl=xy KHt)=<3+,2t=-37 for

A: r(t)=&lt;3t,2t-3&gt;=&lt;0,-3&gt;+t&lt;3,2&gt; x(t)=3t  and y(t)=2t-3 ds=32+22dt=13dt 0≤t≤1

Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. I (a) √(x…

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Q: 1. Evaluate the given line integral, | (x – y, y) · dR, where C is the left part of x² + y? = 1 from…

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Q: Verify Green's Theorem by evaluating both integrals ам √₁ y ² dx + x² dy = √₂√ √ (³x - dA ax ду for…

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Q: Suppose F(x,y)=(4x+6y)i +(6x+4y)j. Evaluate the line integral for each of the given paths, which are…

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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: Q#03(a): Use Green's theorem to evaluate the line integral f. (x – 3y) dx (4x + y) dy, where C is…

A: Green's theorem

Q: Verify Green's Theorem by evaluating both integrals ƏN [_y² dx + x² ay = [] (ax - 3+²) da d'A dy ay…

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Q: Verify Green's Theorem by evaluating both integrals aM | y? dx + x² dy = dA ax for the given path.…

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Q: Evaluate the line integral ſ. 3(x – y) ds along the path C:r(t) = ti + (2 - t)j, 0<t<1

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Q: Evaluate each of the following line integrals. x dy – y dx, 2n <t< 4TT (a) c(t) = (2 cos(t), 3…

A: According to the given information it is required to calculate the line integral. For part (1)