Let C be a circle lying in the plane x+ z = 2 with center at (1,0, 1). Evaluate the line integr V2 dy + -y 1 z dx + 2(z- 1)2 + y2 dz. 2(x – 1)2 + y?

Q: Use Green's Theorem to evaluate the line integral ∫c ( x − y ) dx + ( x + y ) dy where C is the…

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Q: Use Green's theorem to evaluate line integral (9y – In(x2 + y2)) dx + (2 arctan( (2)) dy, where C is…

A: Green's theorem defines that : for ∮CPdx-Qdy there is an integral exists of ∫D∫∂Q∂X-∂P∂Y.dA Here,…

Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

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Q: Find an equation for the tangent plane to the surface z = 6x3y2 + 3y at the point P(1, -3). Hint:…

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Q: Evaluate the line integral y = x² from (-1, 1) to (1, 1) and the line segment from (1, 1) to (−1,…

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Q: Calculate F - dS where F (e* sin y, e² cos y, yz²) S is the surface of the box bounded by the planes…

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Q: Suppose F(x, y) = (3x – 2y)i + 3xj and C is the counter-clockwise oriented sector of a circle…

A: Given, F→(x,y)=(3x-2y)i→+3xj→ Here, M=3x-2y and N=3x radius=3 θ=π3 Limits are 0≤r≤3 , 0≤θ≤π3

Q: Find the circulation of F(x, y, z) = (-y sin 2, x sin z, xy cosz +12) around the circle cut from the…

A: Given that,F(x, y, z)=(-ysinz, xsinz, xycosz+12) around the circle cut from the sphere x2+y2+z2=5 by…

Q: the surface z = &x + 4y th=

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Q: Can you show the steps on how to do this integral?

A: Consider the provided question, (3) Evaluate the integral by using the greens theorem,

Q: 1. Let C be a path along the upper half of a circle from the point P(2,0) to the point Q(-2,0).…

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Q: Let C be the positively oriented circle x2 + y² = 1. Use Green's Theorem to evaluate the line…

A: Given: C is a positively oriented circle x2+y2=1.  Objective of the question is to calculate…

Q: Sketch the space curve r(t) = ⟨2 sin t, 5t, 2 cos t⟩ and find its length over the given interval [0,…

A: The given equation of space curve is  r(t) = ⟨2 sin t, 5t, 2 cos t⟩.

Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: Determine the projection of the following surface on the xy plane. (xy trace) 4z-목 + =0

A: here first solve the given surface and then we trace it

Q: Evaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane…

A: In polar coordinates

Q: Calculate F - dS where F = (e² sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. p x2y dx,…

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Q: Calculate F- dS where F = (e" sin y, e* cos y, yz²) S is the surface of the box bounded by the…

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Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

Q: Evaluate the integral [(3x – 2y + z)ds where C is the curve, C, and C, as shown. 3 y²+ z² 2 G 2* 3…

A: Given that ∫c3x-2y+zds. The objective is to find the integral value. ∫c3x-2y+zds=∫c13x-2y+z…

Q: • Use Green theorem to evaluate the Line integral $(x-3y) da +(42+y) dy whe re C, the Yectungle with…

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Q: Evaluate the line integral g. y³ dx – x²dy, where C is the positively oriented circle of radius 2…

A: Solved below.

Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

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Q: Use Green’s Theorem to evaluate the line integral   ∫_c  (x+ 2y^3)dx + (2x − 3y)dy   where C is the…

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Q: lad Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary of the semi annular…

A: Given Problem:- Use Green's theorem to evaluate ∮cy2dx+3xydy where c is the boundary of the semi…

Q: Let F (tanx + y)ĩ + (x + secy)j and C be the boundaries of the ellipse 9y=9 in the counterclockwise…

A: Given - F→ = tanx + yi^ + x + secyj^ and C be the boundaries of the ellipse x2 + 9y2 = 9 in the…

Q: = xyz exists over a surface S c ed by the plane x-0,y%3D0,z%3D0, z=y V dS over the curve surface.

A: Given:  V= xyz x2+y2=9 To find: ∫s V ds  For solving the convergence x2+y2=9 (mod 1s) we use Chinese…

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A: Given line integral is,

Q: Calculate F - dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: Given F¯={exsiny,excosy,yz2)

Q: Find the integral fc ez dz where C is the circle |z| = 3 in CCD. (z – 1)2(z – 2) %3D -

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Q: Let C be the curve y = 6x³ for 0 ≤ x ≤ 1.3. 13- 12- 11 10- 9- 8- 7- 6- 5- 4 3- 2- 0.5 a Find the…

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Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: Sketch the trace curves of x^2 − y^2 + z^2 − 4x + 2z = 4, and use these trace curves to sketch the…

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Q: Evaluate F-di where F(x, y, z)=1li +(x+yz)j+(xy- Vz 3x+2y+z=6 in the first octant. C is a positively…

A: Here we have to evaluate ∫CF→·dr→=? Where F→(x,y,z)=i^+(x+yz)j^+(xy-z)k^ and C is the boundary of…

Q: : The curve C is intersecting by 12r² +9y? = 36 cylinder and - V3r plane from the point (0, 2,0) to…

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Q: (b) Consider F(x, y) = -i+ j, where (x, y) # (0, 0). x²+y2 x2+y2- Without using Green's Theorem,…

A: Consider the provided function,

Q: Let F (tan-(3x) + y)i + (2x + sec-ly)j and C be the boundaries of the %3D circle x? + (y- 4)2 = 9 in…

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Q: Let Ci be the rectangle with vertices (0,0), (2,0), (0,1), and (2,1) oriented counterclockwise, and…

A: Let C₁ be the rectangle with vertices (0,0). (2,0), (0, 1), and (2,1) oriented counterclockwise, and…

Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

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Q: # 4. Use Green's Theorem to evaluate the line integral P (y*dx +2xy° dy), where C is the positively…

A: Given integral is, ∮Cy4dx+2xy3dy

Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

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Q: Let M(x, y) = y - cos y and N(x, y) = x sin y. Use the Green's Theorem to calculate the line…

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Q: Evaluate the unoriented line integral +y² + z²) ds along the parametric curve a : [0, 1] → R³ with…

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Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

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Q: 3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively…

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Q: Evaluate y dx+3xy dy, where C is the boundary of the semiannual region D in the upper half-plane…

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Q: 7. Find the area of the portion of the plane z = 2y that lies directly above the circle x +(y-1)² =1…

A: we have to find area of the portion of plane .and coverting the problem in polar coordinate makes it…