• Use Green theorem to evaluate the Line integral $(x-3y) da +(42+y) dy whe re C, the Yectungle with vertices (230), (3,0), (3,2) ,(2,2)

Q: Let F = 4(x + y) i + 6 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

A: Let F = 4(x + y) i + 6sin(y) . Find the line integral of F around the perimeter of the rectangle…

Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise.…

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Q: Let F = 4(x + y) i + 8 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

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Q: Use Green's theorem to evaluate the line integral |F•dš where F = 2xyi +(x – y²)j and C is the C…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. | yex…

A: To evaluate the given line integral along the given positively oriented curve. ∫Cyexdx+2exdy Where C…

Q: Evaluate the line integral of f(x,y) along the curve C. f(x.y) = y +x, C: the perimeter of the…

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Q: Jse Green's theorem to evaluate line integral | V8 + x3 dx + 9xy dy where C is a triangle with…

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Q: 1. Compute the line integral (circulation in this case) of F(x, y) around the unit circle C starting…

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Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. 2x + 3y dx + e…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. yex dx…

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Q: Calculate the line integral fe F. dr, where F = (ry, x² + y² + z², yz), and C is the boundary of the…

A: Given F→=xy,x2+y2+z2,yz and C is the boundary of the parallelogram with vertices…

Q: Consider the curve C between the points (1,0, 1) and (0, 1, 1) at the intersection of the cylinder…

A: To evaluate the line integral along with the curve c of ω=−ydx+xdy+dz.

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. yex dx…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. yex dx…

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Q: Calculate the scalar line Integral where the function is f(x,y)= 1 / x²+y²+1 and the curve is the…

A: We have given function fx,y=1x2+y2+1 and the curve joining the point 0,0 1,0 1,1 0,1. Let A0,0,…

Q: Use Fubini's theorem to compute the double integral R f(r, y)dA where f(r, y) = 2x²y+ ry-2 and…

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Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise.…

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Q: 4. Using Stokes's theorem, calculate the line integral F dr, where F = [2y, 3z, z - z) and C %3D is…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. yex dx…

A: Formulae used, d(ex)dx=ex d(x)dx=1and         ∫abexdx=exab

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Q:4) Use Green theorem and evaluate the line integral ${Mdx + Ndy} Where M(x,y)=y², N(x,y)=x², C is…

A: See the details solution in below

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. yex dx…

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Q: Calculate the line integral of F(x, y, z) = (e², e*-", e') over the closed path ABCA, where A C =…

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Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

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Q: (a) Find the line integral of f (x, y, z) = -x + y + z over the straight-line %3D segment from (1,…

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Q: compute the line integral fc f (x, y) ds for th,e given function and path or curve. (a) f (x, y) =…

A: To compute the line integral  ∫Cfx,y ds where, fx,y=xy and the path of curve is rt= t,  2t-1…

Q: Use Štoke's Theorem to evaluate the line integral - 2ydx +-6zdy + dz where C is the intersect | of…

A: Strokes theorem is ∫CF→.dr→=∫∫S∇×F→.N→dS=∫∫ScurlF→.N→dS x=rcosφy=rsinφ

Q: Consider out counterclockwise. fo x²y dx - xy² dy, where C is the boundary of the region 0 ≤ y ≤ √√4…

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Q: Use Green's Theorem to evaluate the line integral.       Cy dx + 7x dy C: square with vertices (0,…

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Q: Let F = 4(x + y) i+8 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. S. cos…

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Q: dri Let F=[4z2, x², 2y?] and C be the positively oriented boundary of the triangle with vertices (0,…

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Q: Use Green's Theorem to evaluate the line integral. Begin by sketching the region S. (e* + 5y) dx +…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C xy2…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [² yex…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve.…

A: Using the Green's theorem.         ∫C  (M dx+N dy)=∫∫D ∂N∂x-∂M∂ydA.    ∴    ∫C y…

Q: Using Green's theorem, convert the line integral §(6y² dx + 2xdy) to a double integral, where C is…

A: Given integral, ∮C6y2dx+2xdy Here C is the boundary of the square with vertices ±2,2 and ±2,-2.…

Q: Use Green's theorem to evaluate the line integral [F•dš where = 2xyi +(x- y')j and C is the path…

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Q: Use Stokes' Theorem to choose the correct integral to evaluate the line integral…

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Q: Let F = 4(x + y) i + 8 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

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Q: 5) Using Green's theorem, convert the line integral .(6y? dx + 2xdy) to a double integral, where C…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve.…

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Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. e5x + 2y dx +…

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Q: 5) Using Green's theorem, convert the line integral f.(6y² dx + 2xdy) to a double integral, where C…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. | yex…

A: Green's Theorem: Let C be a simply connected piecewise smooth curve with a positive or counter…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. |…

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Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…

Q: Evaluate the line integrals using the Fundamental Theorem of Line Integrals: ∫c (yi+xj)*dr Where C…

A: Introduction: One method for extending this theorem into higher dimensions is the gradient theorem,…

Q: Let F = ( ) and y = {x² + (y – 2)²) = 1 with anti-clockwise orientation. Find line integral , F. ds.…

A: Put x = cost  dx = -sint dt y=sint+2   dy = cost dt int(f.ds)  = int (  y/(x^2 +y^2) dx -…

Q: that the in tegral is inde pen dent the path, and v6e S how the Fundamental to of of Line Integrals…

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