O Evaluate the line integral over The Cur ve C. SCx+y+2)dx +6x +y-2)dy+ (x-y+2)dz where c is the line segment fiom (-1,2, 3) to (3,-2, 1).

Q: Please solve the line integral Se F · dĩ In where: F = y²i+2r(y+1)j Is along 2 unique paths from the…

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Q: Compute the double integral of (x – 2y) Væ + 2y o i over the quadrilateral with vertices (0, 0), (4,…

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Q: Evaluate the double line integral S  of the fuinction (x − 2y + z) dS. S: z = 9 − x,  0 ≤ x ≤ 9,  0…

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Q: Find the line integral of f (x, y,z) = -x + y + z over the straight-line segment from (1, 2, 3) to…

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Q: Evaluate the line integral along the given path: 1. So ry ds, where C : r(t) = 4ti + 3t²j, 0 < t <…

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

A: To find the line integral we use the equation of line segment in parametric form using given points.

Q: 2) Evaluate the following line integral: . 0+z)dx + (x + z)dy + (x + y)dz where C consists of the…

A: C1: (0,0,0) to (1, 0, 1)x-01-0=y-00-0=z-01-0=tx=t, y=0, z=tdx=dt, dy=0, dz=dtI1=∫01[(0+t)+(t+0)]…

Q: Evaluate the line integral, where C is the given cu curve. (x + yz) dx + 2x dy + xyz dz, C consists…

A: C consist line from A (2, 0, 1) to B(3, 3, 1) Now,

Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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

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

A: Introduction: The formula of line integral of the function f(x,y) on the line segment C(t) is given…

Q: Compute line integral of F(x,y) = (2x² – 3,₁²³)^² + (2x +34²) ↑ с over the following C F-dr SCF ¾ ç…

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Q: Find the line integrals of F = 4yi + xj + zk from (0,0,0) to (1,1,1) over each of the following…

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Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy'dy, where C is the triangle with…

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Q: Evaluate the line integral of x^3(z)ds, where C is the line segment from (0,8,2) to (7,4,6).

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Q: Is dz

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Q: 5. Evaluate the line integral (r+2y) dr+x² dy where C consists of line segments from (0,0) to (2, 1)…

A: In order to solve this question by the formula of line integral .

Q: Evaluate the line integral / x°z ds, where C is the line segment from (0, 2,4) to

A: Line integral: - The function to be integrated is determined along a curve in the coordinate system…

Q: Evaluate the line integral ∫c x3 z ds, where C is the line segment from (0,8,8) to (5,7,6).

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Q: Calculate the line integral F(x, y, z)=2xy^2 i+(2yx^2 +2y)j     on a path from (0, 0, 0) to(3, 1, 1)

A: We need to compute the line integral: F(x,y,z)=2xy2i+(2yx2+2y)j on a path from the point: 0, 0, 0 to…

Q: Evaluate the given line integral. I (y, –x) · dR, where C consists of 4y = x² from (-2, 1) to %3D C…

A: Line integration of the function

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: Evaluate the line integral given in the figure below

A: Given question is belongs to the vector calculus and from the line integration we have to integrate…

Q: Set up an integral for the length of y = vx + 2, 2 2 <x<7 using ds = 1+ ) dy. A. ds = f, /1+ 4y²dy…

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Q: 1. Evaluate the line integral f(z, y) ds where f(x, y) = Vx+ 2y and C is the straight-line segment…

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Q: Verify the Green's theorem for integral x²y dx + xy dy, where C is the boundary described…

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Q: Use Green's Theorem to evaluate the line integral S(x² + y²)dx + (x² – y²) dy where C is the…

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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: Find the line integral of f(x,y,z) = -x+y+z over the straight-line segment from (1, 2, 3) to (0, −1,…

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Q: 7. Verify Green's Theorem for O (6 +2) dz + (1 – 2ry) dy where C is shown below by (a) computing the…

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Q: Find the line integral of F = 2√√zi-4xj + 3√yk, from (0,0,0) to (1,1,1) over each of the following…

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Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy*dy, where C is the triangle with…

A: The given triangle C with the vertices (0,0),(1,0) and (1,2) is as as shown below.

Q: Find the line integral of F= 2√zi-4xj + 3√√yk, from (0,0,0) to (1,1,1) over each of the following…

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Q: |Evaluate the line integral: f.(r² + y) dx + (4x – cos(y)) dy where C is the boundary of the square…

A: According to Greens theorem, the line integral ∮CPdx+Qdy=∬DQx-PydA. BY the extended version of…

Q: Find the line integral of f(x,y,z) = -x + y+z over the straight-line segment from (1, 2, 3) to (0,…

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Q: a) Evaluate the line integral S. (2x – y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

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

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Q: 4. Use Green's Theorem to evaluate the line integral: f ye dx + x*y² dy, where C is the from (-2,0)…

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Q: Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i +…

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Q: 6- Evaluate the line integral fF dr, where F = [xy, yz, xz] and C is the boundary of the hemisphere…

A: the line integral f F dr, where F = [ry, yz, xz] and C is the boundary of the hemisphere x² + y² +…

Q: (1) Evaluate the line integral of F (x, y) = (x – y, x²) over the line from (1,0) to (3, 2). |

A: evaluate line integral in following way

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

A: Using parametric equation, line integration is evaluated.

Q: Find the line integrals of F = yi + 3xj + zk from (0,0,0) to (1,1,1) over each of the following…

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Q: Use the Fundamental Theorem of Line Integrals to evaluate fo F·dR, where F(x, y) = (x²y² – 3x, r³y)…

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Q: #1. Evaluate (2x – 5y) dA, R where R is the parallelogram with vertices (0,0), (2,3), (–1,4) and…

A: The given region R is a parallelogram with vertices as shown in below graph. We have to use change…

Q: Evaluate the given line integral. | (y, -x) dR, where C consists of 4y = x² from (-2, 1) to (2, 1)…

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Q: Calculate the value of the line integral fds where f(x,y,z)=e² and C is described by C (x, y,…

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