Find the work done by the force field F in moving an object from P to Q. F(x, y) = e-Y i – xe-Y j P(0, 6), Q(8, 0)

Q: 12. Calculate the work done by the by the force field, F, along the curve r(t). F = (y – a²) i+ (z –…

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Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 4y³/2 i + 6x√y j…

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Q: Find the work done by the force field F(x,y) = x² i– 2xy j in moving a particle along the quarter…

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Q: Find the work done by the force field F in moving an object from P to Q. F(x, y) = x°i + y°j; P(1,…

A: Here, the objective is to find the work is done by the force field F in moving an object from P to…

Q: For the force field given by F(x, y, z) = e cos yi – e sin yj + 2k show that f. F. dr is independent…

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Q: 20

A: I have stated the used formulas in the solution

Q: Find the work done by the force field F in moving an object from P to Q. F(x, y) = x³i + y³j; P(1,…

A: The force field F can be represented as the gradient of the potential field. Work…

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Find the work done by the force field F in moving a particle along the curve C. F(x, y) = (x - y°)i+…

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Q: Find the work done by the force field F(r, y) = x²i+ xyj on a particle that moves once around the…

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Q: Find the work done by the force field F(x, y, z) = xyi+ yzj+xzk or a particle that moves along the…

A: Given: Fx,y,z=xyi+yzj+xzkr(t)=ti+t2j+t3k

Q: (b) Given the force field F(x, y, z) = (z³ – 2xy)i – x²j + 3xz² k (i) Show that F is a conservative…

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Q: Find the work done by the force field F on a particle that moves along the curve C. F(x, y) = (2x +…

A: Formula: The work done by the force field F that moves along the curve C is: W=∫C F·dr Suppose the…

Q: Find the work done by the force field  F(x, y, z) = y + z, x + z, x + y  on a particle that moves…

A: Given that the force field,

Q: Determine the work done by the force field F(x, y, z) = (x − y2, y −z2 , z − x2) on a particle that…

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Q: Find the work done under the influence of the force E = 3xyi – 5zj + 10xk along the curve x= t² + 1,…

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Q: How much work is required to move an object in vector force field F = (yz, xy, xz) along path r (t)…

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Q: Find the work done by the force field F = (y-x)i + (z- y?)j + (x - z)k along the curve r(t) = ti +…

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Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 6y3/2 i + 9xyj…

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Q: Find the work done by the force field F(x, y, z) = (x - y2, y – z2, z - x2) on a particle that moves…

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Q: Find the work done by the force field F(x, y, z) = (y + z, x + z, x + y) on a particle that moves…

A: It is known that

Q: Consider the force field F = (ev – e2" , (x + })ev) and the curve C = C¡U C2 where Cı is the line…

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: Find the work done by the force field F(x, y, z) = (x – y², y – z?, z – x2) on a particle that moves…

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Q: Exercise (3): Find the work done under the influence of the force F = 3xyi – 5zj + 10xk along the…

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Q: Find the work done by the force field F→(x,y)=54x^2y^2i→+(36x^3y−2)j→in moving an object from the…

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Q: Find the work done by the force field F in moving an object from P to Q. F(x, y) = e-Y i - xe-Y j…

A: Given that, Vector field is, F(x, y) = e-yi - xe-yj The points are, P(0, 8)  and  Q(2, 0) We have to…

Q: Find the work done by the force field F(x, y, z) = (x − y², y - z², z - x²) on a particle that moves…

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Q: Find the work done by the force field F(x, y) = xi + (y + 7)j in moving an object along an arch of…

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Q: find the work done by the force field F(x,y) =(2y+x²,x²-2x) acting on an object as it moves along…

A: Given: The force field, Fx,y=2y+x2,x2-2x.   To find: The work done by the given force field acting…

Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 6y3/2 i + 9x…

A: Here we use the formula

Q: Find the work done by the force field F(x, y, z) = (y + z, x + z, x + y) on a particle that moves…

A: Given To find the work done by the force field Fx,y,z=(y+z,x+z,x+y)  on a particle that moves along…

Q: Consider a particle that moves through the force field F(x, y) = (y - x)i + xyj from the point (0,…

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Q: a. Find the work done by the force field, F(x, y) = x²i – xyj in moving a particle along the…

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Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 2y3/2 i + 3x/ỹ j…

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Q: Find the work done by the force field F(x, y) = x 2 i yex  on a particle that moves along the…

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Q: Without using a potential function, find the total work performed by the force field F(x,y) = (2xsin…

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Q: Find the work done by the force field F in moving an object from P(-9, 7) to Q(3, 3). 2.x. F (r, y)…

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Q: Find the work done by the force field F in moving an object from A to B. F(x, y) %3D 2y3/2 i + 3x/у…

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Q: Find the work done by the force field F(x, y, z) = xy i+ yzj+xzk on a particle that moves along the…

A: Solution is given below:

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y) = xi +…

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Q: Without using a potential function, find the total work performed by the force field F(x, y) =…

A: Work done by vector field while moving a particle along a curve = Line integral of that vector field…

Q: Find the work done by the force field F(x, y, z) = 5xi+5yj+4k on a particle that moves along the…

A: Given

Q: Find the work done by the force field F in moving an object from P(-9, 5) to Q(3, 5). F (r, y)

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Q: Find the work done by the force field F in moving an object from A to B. F(x, y) = 2y3/2 i + 3xVyj…

A: As per guidelines, we will solve the first question only.

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A: Introduction: When we apply force 'F' to a block, the body accelerates or speeds up or down…

Q: Find the work done by the force field F(x, y) = xyi+ x²j on a ,2 particle that moves along the curve…

A: Consider the given force field Fx,y=xyi+x2j Then, F⇀x,y=xy,y Write in parametric form y=t  then…

Q: Find the work done by the force field F(x,y) = x²yi + y²j around the circle with radius 2.

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Q: Find the work done by the force field F in moving an object on the line segment from A to B, where…

A: Given, Fx,y=2y32 i +3xy j To find the work done by the force field F in moving an object on the line…

Q: Find the work done by the force field F(x,y)=xi+(y+5)j in moving an object along an arch of the…

A: Work done can be estimated by integrating the F( r(t) ) from t = 0 to t = 2π

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: