Let F(x, y) = (2x + e – y cos? x, xel + sin y). Let C1 be the path from (0,0) to (7,0) along the x-axis, and let C, be the path from (7,0) to (0,0) along the graph of y = sin r. (a) Evaluate the line integral F. dR. C1 (b) Let C = C¡ U C2. Use Green's Theorem to evaluate (c) Use the results in parts (a) and (b) to find the amount of work done by F in moving an object along C2.

Q: evaluate the line integral along the curve C. Scv+z) d s, C is the straight-line segment x = 0, y =…

A: To Evaluate∫C(y+z)dswhere C is straight line segmentx=0  ----(i)y=3-t -----(ii)z=t…

Q: Calculate the integral O (y – e*) dx + (3x + e') dy where L is along the curve x + y´ : = /x2 + y² -…

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Q: 2- Show that the function is analytic everywhere except at the points z +i += and on the half line…

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Q: 1. Calculate the line integral f F-d7, where F (z. y, 2) = -y? +z3 +zk and C is the path C along the…

A: This is a problem from line integral.

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A: Line integral

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Q: Evaluate the line integral I of the one-form w = (y+ z) dx + (x + z) dy + 10z dz over the line…

A: We have to find the line integral.

Q: Evaluate the line integral F· dr where F (3 sin z, -5 cos y, 5cz) and C is the path given by r(t) =…

A: Line integral is integral of some function along a curve or path. Any field for which the line…

Q: Let f( x , y , z ) = x 3 y 2 - y 3 z 2 + sin(x + y)cos(x + z). Determine the line integral of f ( x…

A: given fx,y,z=x3y2-y3z2+sinx+ycosx+z arc length rt=cos2πt,sin2πt,t0≤t≤2

Q: Evaluate the line integral, where C is the given curve.   z2 dx + x2 dy + y2 dz,   C C is the line…

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Q: Evaluate the line integral , F dr where F (3 sin x, -5 cos y, xz) and C is the path given by r(t) =…

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Q: Calculate the integral of f(x, y, z) = 3x² + 3y² + zª over the curve c(t) = (cos t, sin t, t) for 0…

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Q: Evaluate the line integral (x+2y)dx + dy, where C consists of the path C from (0,0) to (3,0), the…

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Q: Evaluate the line integral J xe" dx +y sin y dy along the triangular path consisting of the line…

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Q: 6. Evaluate the line integral (x? + y² )dx – x dy along the curve C: x? + y² =' counterclockwise…

A: Given: ∫c x2+y2 dx- x dy  We have to Evaluate the given line integral along the curve C: x2+y2=1…

Q: Calculate the integral (x – y) dx + (x + y) dy I = x2 + y2 where L is along the curve y = cos x,…

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

A: Given: fx,y=x-y To Find: Line integral ∫Cfx,yds over the unit semi-circle x2+y2=1, y≥0

Q: Find the line integral of F(x, y, z) = x³i + yj+ zk along th the origin to the point (3, 2, 6). F.…

A: See the details solution in below

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

A: Our Aim is to evaluate the line integral along the given positively oriented curve xy2 dx+3x2y dy…

Q: Calculate the integral =| [e* sin y – b(x + y)] dx + (e* cos y – ax) dy where a, b are constants, L…

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Q: Let f(x,y) = x 3 + y 4  + sin(2x+3y) . Determine the line integral of f(x,y) with respect to arc…

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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 path…

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Q: Evaluate the integral [(e' - y)dx + (sin y +x)dy using Green's theorem where C is 16 bounded by y =…

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Q: B) Evaluate the line integral of the function P(x,y) dx + Q(x,y) dy. over the curve C where…

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Q: Evaluate the line integral | F•ds where F = 2xyi + (x – y²)j and C is (a) y = x from (0,0) to (1,1)…

A: For the solution follow the next steps.

Q: Let f(x,y) = 3x 2 y + e x+2xy . Determine the line integral of f (x,y) with respect to arc length…

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

A: The objective of the question is evaluate the definite integral.

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Q: Evaluate the line integral along the given paths.       C(x2 + y2) ds   a) C: line segment from (0,…

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Q: Consider the following line integral. xy dx + x²y dy, Cis counterclockwise around the triangle with…

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Q: Consider the line integral xy dx + xy° dy with C the triangle with vertices (0, 0). (1,0), and (1,…

A: Given, the line integral Where C is the triangle with vertices.

Q: Q5 Use Green's theorem to evaluate the line integral (cos.x+2y)dx+(x – sin y)dy C where C is the…

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A: To find the equivalent double integral we will use the Green's Theorem also we will draw the…

Q: Evaluate the line integral along the given path. (x² + y² + z?) ds C: r(t) = sin(t)i + cos(t)j + 5k…

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Q: The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3…

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Q: Question attached thanks!

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Q: (b) Let F(x,y) = (e2*y+cos(7x²), xºy^+e>Y³} Use Green's Theorem to set up the line integral F. dr as…

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Q: Evaluate the line integral | F•ds where F = 2xyi +(x – y²)j and C is (a) y=x from (0,0) to (1,1) (b)…

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Q: The area of the surface obtained by rotating the curve y = 1 < x s e about the line x = 24 is O 2n…

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

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Q: Evaluate the line integral f F · dr, where F(x, y, z) = –2xi + 3yj + 3zk and C is given by the vecte…

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Q: Let R:x²<ys 3 be the closed region having boundary C with counter-clockwise orientation. F=[X…

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Q: Let f ( x , y , z ) = x 3 + y + z + sin(x + z) + e x-y . Determine the line integral of f ( x , y ,…

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Q: Evaluate the line integral , F. dr where F = (3 sin x, -5 cos y, xz) and C is the path given by r(t)…

A: To determine the value of the integral.

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Q: 20. Given the path, x $ dx + xe dy determine the line integral using Green's theorem if C₁is y = x²…

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Q: Evaluste the line integral using Green's Theorem and check the answer by evaluating it directly.…

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Q: 20. Given the path, dx + xey dy determine the line integral using Green's theorem if C₁is y = x² +…

A: Given, ∮Cxydx+xeydy To determine the line integral using Green's theorem if C1 is y=x2+2, with the…

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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