Compute the line integral | (yze*v= + y° + z - 2x) dr + (xze*# + 2ry) dy + (rye#"= + x + 32²) dz, where C is the curve in space with the parametrizations for 0 < t<1: r(t) = sin(at'24) +t!³, y(t) = t - to + 4, z(t) = t'1500 cos(at1830) + 1. 2021

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 unoriented line integral (22 + y° + z²) ds (2x² along the parametric curve a : [0, 1]…

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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 evaluate the line integral |F•dš where F = 2xyi +(x – y²)j and C is the C…

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Q: (a) Evaluate ([ Á.ds where A=(x+y²)î-2xj+2yzk and s is the surface of the plane in the first octant…

A: For the detailed solution of the problem follow the next steps.

Q: Exercise 10.6 Evaluate the line integral using a method of your choice. e¯*(cos y dx + sin y dy),…

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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: Calculate the line integral [(of).do where f(x, y, z) = x ² ¹² + 4 xy² z yz с + е хуча and C is the…

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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: 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: 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: Evaluate the line integral / V(ry + xz + yz) · dĩ over the curve F(t) = (t, 2t, 3t) for 0 <t < 4…

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Q: Use Green's Theorem to evaluate the line integral: f. In(1 + y) dr – #, dy where C is triangle with…

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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: Compute the line integral of the scalar function f(x,y,z)=2x2+8zf(x,y,z)=2x^2+8z over the curve…

A: To find the line integral, obtain dS as follows.

Q: Let f(x, y, z) = (2x + 4z + 10)/xy + 2. %3D a. Evaluate the line integral of f along the line…

A: We will find out the required solution.

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 line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0,…

A: Given: ω=xydx+12ydy To find: I=∫αω  where α:[0,ln2]→ℝ2 with α(t)=(e2t,e-2t) ∴x=e2t,y=e-2t Now,…

Q: Evaluate the line integral (direct method) | (3x– y) dx – x dy , where C consist of the parabola…

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Q: Let f(x, y, z) = (2x + 4z + 10)/xy + 2. %3D a. Evaluate the line integral of f along the line…

A: We will evaluate the given integral.

Q: Evaluate the line integral Fdr where F = 4.xyi – 8yj+ 3k and C is a curve given by y = 2x, z = 3…

A: Answer

Q: Consider the curve C consisting the the portion of the parabola y = x² from (2, 4) to (-2, 4)…

A: Given: 1. y=x2 Answer:(a) positively oriented since its upward and line joining is positive sides

Q: Evaluate the line integral (direct method) |(3x– y) dx – x dy , where C consist of the parabola y=…

A: Given integral is, ∫C(3x-y)dx-xdy

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: Given the scalar function f(x,y)=2xy,calculate the line integral along the ellipse curve from point…

A: Given data:- The given curve is, x29+y24=1 The given scaler function is, f(x,y)=2xy t E 0,π/2

Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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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 along the given positively oriented curve. [(5y +…

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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: Use the Green's Theorem to evaluate the line integral 2xydx + x² – y² dy where C is the curve…

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Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

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Q: 8.) Find work done by F = (2x³y* + x, 2x*y³ + y) along the path r(t) = (t cos(at) – 1, sin (t))…

A: Since we have given that F = 2 x3 y4 +x, 2 x4 y3 +y   and rt=t cosπt-1, sinπ2t    drt = cosπt -t…

Q: 6. Use Green's Theorem to evaluate the line integral fc 2xy dx + (x² + y²) dy, if C is the ellipse…

A: Let R be simply connected region with a piecewise  smooth boundary  'C'. If functions 'M' and 'N'…

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: Use Green's theorem to evaluate the line integral F•ds where F = 2xyi +(x-y')j and C is the %3D path…

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Q: Compute the scalar line integral xy ds where C is the part of the circle of radius 3, centered at…

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Q: . Apply Green's Theorem to evaluate the given integrals: a. 2x +y)dx + (2xy = 3y)dy where Cis any…

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Q: Let F = yi + xj + x³y³ z³k, C the curve x2 + y² + 6x – 2y + 9 = 0, z = 2 (with counterclockwise…

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Q: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 8y dx…

A: Introduction: Green's theorem is one of calculus' four fundamental theorems, all of which are…

Q: Use Green's theorem to evaluate the closed line integral: . x²y dx +x'y dy along C between -1 < x< 2…

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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: Let C be the intersection curve of the paraboloid z = x2 − y2/2 with the cylinder x2 + y2 = 1,…

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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: Compute the line integral (yze"y= + y² + z – 2x) dx + (xze"v² + 2xy) dy + (xye"y= +x+ 3z²) dz C…

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Q: Verify Green's theorem in the plane for (3x² -8y²)dx+(4y-6xy)dy, where C is the closed curve of the…

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Q: A) if F=2yi-zj+xk evaluate line integral Fxdr along the curve x=cost,y=sint,z=2cost from t=0 to…

A: Given x = costy = sintz = 2cost As F = 2yi-zj+xk Then F(x,y,z) = 2y , -z , x Thus F(x(t) , y(t) ,…

Q: Compute the line integral [(yze²v² + y² + 2 − 2x) dx + (xze²v² + 2xy) dy + (xye²³² +x+32²) dz, where…

A: We have to compute the line integral ∫Cyzexyz+y2+z−2xdx+xzexyz+2xydy+xyexyz+x+3z2dz, where C is the…