Find the work done by the force field F in moving an object from A to B. F(x, y) = 2y3/2 i + 3xVyj %3D A(1, 1), B(2, 4)

Q: The given vector function is F(x, y, z) = (2x – y + In(z² + 1))î + (x – 6e²y + 4 cos 4y)ĵ + | 2xz -…

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Q: Sketch the following vector fields (a) F(x, y) = 2i+xj (b) F(x, y) = 2xi + 4yj (c) F(x, y) = Vf…

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Q: Let r(t) = (e", e", te") be a vector function. Find; 21 -2t (a) r'(1) (b) r"(1) %3D

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Q: Find the work done by the force field

A: Given: The given function is, With A(1,1) and B(4,4). To find: The work done by the force field F…

Q: Find the work done by the force F = xyi + (y − x)j over the straight line from (0,0) to (2,2).

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Q: Given that r(t) is a vector function that satisfies the following: r'(0) = . Find the value of 'c'…

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

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Q: Find the work done by the force F = xyi + (y − x)j over the straight line from ( − 1,0) to (0, − 1).

A: In the given problem, force is given and the displacement straight line is given. We have to find…

Q: Q4. Simplify the following expression: 3-5 x 39 Click on image to enlarge if needed 12 81 243 324

A: To evaluate :- 3-5 * 39

Q: The number of houses that can be served by a water pipe varies directly as the square of the…

A: Given that, The number of houses that can be served by a water pipe varies directly as the square of…

Q: Utilize Green's Theorem to figure out the work done by the force: F(x, y) = x(x + 3y)i + 3xy²j in…

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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 + 9x√yj…

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Q: A particle moves in the positive direction once around the square with vertices (0, 0), (0, 2),(2,…

A: Given, the force field Fx,y=x-sinxi+y2+xj. We have to find the work done.

Q: - 25y,0,) 10- through the surface Find the outward flux of F =1.

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

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Q: Find the work done by the force field F(x, y) = y² 7 + (x²-4) j to move a particle along the portion…

A: We shall plot the curve over which we have to perform the integration.

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: