If a vector function v(t) = (t, In t , t¯²) is given for a scalar function Ø = x In z + Jy– cos(x + 1) from t = 3 to t = 2m, determine the line integral. A. 46.0051 sq. units B. Diverging %3D C. 49.0271 sq, units D. -9.3813 sq. units

Q: Evaluate the line integral F· dr, where F(x, y, z) = 3xi – 2yj – 4zk and C is given by the vector…

A: Given that F→=3 xi→-3 yj→-4 zk→ r→=sin t i→+cos t j→+t k→ and t is varying from 0→ 3π4  then x=sin…

Q: Compute the line integral of the scalar function f(z,y, 2) = 2z² + 8z over the curve c(t) = (e*, t²,…

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Q: If C is the curve given by r (t) = (1+2 sint)i+ (1+ 2 sin? t)j+ (1+1 sin' t) k, 0<t< and F is the…

A: Given:

Q: Given the following vector field and oriented curve C, evaluate F•Tds. C F = (x,y) on the parabola…

A: Given that, Fx,y on the parabola rt=4t,9t2 for 0≤t≤1. Obtain the r't. r't=ddt4t,9t2=4,18t

Q: (a) Given the vector field F = xy + 2yzý + 3zx 2, calculate the line integral around the closed path…

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Q: Evaluate the line integral , F · dr,  where C is given by the vector function r(t). F(x, y, z) =…

A: F and vector function r are given as,

Q: Find the value of the line integral ∫CF→⋅dr→if F→(x,y)=(y^3+11)i→+(3xy+11)j→is a conservative vector…

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

A: Given F(x,y,z)=xi-yj+3zk and C is the curve given by  rt=sint,cost,t. Find ∫CF·dr.

Q: Which of the following is the integral that gives the length of the curve defined in vector form as…

A: First I have written the definition of length of a curve in parametric form, just use that…

Q: Q3 Given the conservative vector field, F =(x +y²)i +(2xy +5)j , evaluate the integral F•ds where C…

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Q: Q3 Given the conservative vector field, F = (x +y²)i +(2xy +5)j , evaluate the integral F•ds where C…

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Q: For the vector field F(x, y, z) = (15x2y + 2xz)i + (5x3 + 35y4)j + x2k, show that F is conservative…

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Q: Let the vector field F be given by F(x,y,z)=(y,xz,=z^2).  Evaluate its integral along the curve C…

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Q: Evaluate the line integral F. dr, with vector field F(x, y, z) = sin xi + cos yj + xz k, and path C…

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Q: 2) Given the vector field F = (- Vx²+y² 2z2) write the integral to calculate the outward x²+y² flux…

A: We have to find the outward flux across the cylinder x2+y2=100.

Q: Given the following vector field and oriented curve C, evaluate F•Tds. F= (x,y) on the parabola r(t)…

A: F=&lt;x,y&gt;, r(t)=&lt;12t,9t2&gt;, 0≤t≤1F(r(t))=&lt;12t,9t2&gt;r'(t)=&lt;12,18t&gt;

Q: Q3. Consider the vector of electric field E(x,y,z) = (sinh x)i – (cosh y)j – xyz k a. Compute the…

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Q: 2. Consider the vector valued funcion In(1 – t) /t+I, e-1/lt| if t +0 R(t) = t (1,0, –1) if t = 0.…

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Q: Evaluate the line integral fF. dr, where F(x, Y, z) = 4xi – 3yj + 3zk and C is given by the vector…

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Q: Compute the line integral of the vector field F=⟨3zy−1,4x,−y⟩ over the path c(t)=(et,et,t)for −4≤t≤4…

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Q: (A) Given the vector function r(t)=( V21,e', e-), the unit normal vector N(t) is of the %3D form:…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the work done by the vector field F = ( – 2, – 4y, 2æ) in moving an object along C in the…

A: Let F be a vector field defined on a smooth curve C whose parametric equation is given by rt, a≤t≤b.…

Q: Consider the motion p(a, t) given by p(x, t) = ((1+t)α₁, a2 + ta3, -ta₂+ α3)² and let f(x, t) = tx₁…

A: Given the motion φα,t=1+tα1, α2+tα3, -tα2+α3T and fx,t=tx1+x2 be an Eulerian scalar field.…

Q: Given the conservative vector field, F=(x +y³)i +(2xy +5)j , evaluate th integral F•ds where C is…

A: We evaluate the given integral by using line integral. We parameterized the curve between two…

Q: Consider the semicircle r(t) = a cos(t)i + a sin(t)j with 0 0. For a given vector field F, the flux…

A: Given

Q: Show that the vector field given below is conservative and find its potential function. F(x, y) =…

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Q: Consider the following vector fields: F = (3x²e²ª, 2x³e²y + 2 cos y sin y) and Ġ = (y+z, x+y, z —…

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Q: Find the flux of the vector field F(x, y, z) =(x)i+(y)j+(z)k through the surface S of the…

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Q: Sketch the vector field F(x, y) = i + 3j and calculate the line integral of F along the line segment…

A: We have to sketch the vector field.

Q: Evaluate the line integral F dr, where C is given by the vector function r(t). F(x, y, z) = sin(x) i…

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Q: F(x, y) = (6xy – 4) i+ (1+ 3x? + In y)j is conservative. (b) Use the Fundamental Theorem of Line…

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Q: 4. Evaluate the line integral Vf-r'dt, where the curve C is given by the vector function r(1)…

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Q: Given the following vector field and oriented curve C, evaluate T ds. F = (x.y) on the parabola r(1)…

A: In this question we will find the line integral of F over c.

Q: Given the following vector field and oriented curve C, evaluate |F•T ds. F= (x,y) on the parabola…

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Q: Find the integral of ſ r(t) dt r(t) for the vector-valued function, = (In(t))i + /1+ cos4t)j + dt k…

A: The integral of any vector function given by, r→(t)=r1(t), r2(t), r3(t) is given by: ∫r→(t)…

Q: Find all potential functions of the conservative vector field F (x, y, z) = (2xz + y², 2xy,x² + %3D…

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Q: Consider the following vector fields: F = (3x² e²y, 2x³e²y + 2 cos y sin y) and G= (y+z, x+y, z —…

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Q: Evaluate the line integral F· dr, where C is given by the vector function r(t). F(x, у, z) sin(x) i…

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Q: Find the work done by the vector field F = (- 3z, 4y, 2x) in moving an object along C in the…

A: Work done by any vector field F is given by ∫F.dr where r is the position vector. Dot product is the…

Q: Let F = x?i+y?j+z²k, S be part of the surface 22 = supplied with the unit normal field i for which i…

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

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Q: Calculate the line integral , F · dr, where C is the straight-line path from (2,0) to (0,2),…

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Q: Consider the line integral a xy dx + yz dy + xz dz. (a) What is the vector field that is being…

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Q: Compute the line integral of the scalar function f(z,y, 2) = 2z² + 8z over the curve e(t) = (e*, t²,…

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Q: Find the path integral of a particle moving along a straightline connecting O(0,0,0) to A(1,1,1)…

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Q: Compute the line integral of the scalar function ƒ(x, y, z) = 2x² + 8z over the curve c(t) = (e¹,…

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Q: Compute the line integral over the vector field F(z, y, 2) = where the curve C is the boundary of…

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Q: Consider the one-form w = x' cos(y) dx + xe13% dy+4z² dz on R3. The associated vector field is: F(x,…

A: For the solution follow the next step.

Q: Find the integral of ſ r(t) dt for the vector-valued function, r(t) (In(t))i + /1+ cos4t)j + dt k…

A: NOTE: The vector-value function is dependent on variable t, so z component of vector function is…