Find the work done by the force F = xyi + (y-x)j over the straight line from (0,0) to (1, - 3). The amount of work done is (Type an integer or a simplified fraction.)

Q: Suppose that 2 J of work is needed to stretch a spring fromits natural length of 30 cm to a length…

A: Stretched distance = 42-30 =12  cm = 0.12 m  Let F=kx [ by Hooke's law ]  So,

Q: A particle is under the influence of the force F= (-cosh (4x4) + xy)i + (e-y + x)j. The corner…

A:

Q: find the velocity and acceleration vectors in terms ofur and uθ .1. r =θ and dθ/dt = 2

A: Given, r=θ and dθdt=2   Find Velocity and acceleration vectors in terms of ur and uθ:

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,- 2) to (2, - 4).

A:

Q: Find the work done by a force F = 5i (mag-nitude 5 N) in moving an object along the line from the…

A: Given,

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,-3) to (3,-9).

A: Given force is F→=xyi^+y-xj^ and straight line coordinates are 1,-3 and 3,-9

Q: Find the work done by the force F in mving an object from P to Q. F = 2i – 4j; P(0, 0), Q(3, 6)

A:

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: Determine the work done by the force F"(x,y,z)=(x²y,xy). to move a particle along the line segment…

A:

Q: Find the work done by the force F = x²yi– xy²j along the paths shown from (1, 1) to (4, 2). (4, 2) a…

A:

Q: Find the acute angle that a constant unit force vector makes with the positive x-axis if the work…

A: Given- a constant unit force vector makes with the positive x-axis if the work done by the force in…

Q: (True/False) Suppose the work done by a force F on a particle moving along a path C is given by x,…

A: True.

Q: Find the work done by a force F of 12 pounds acting in the direction (3,1) in moving an object 8…

A:

Q: Show that the force F = (y^²2² - 6xz² ) ₁² + ²xyz²³ j^² + (3 xy² z ²-6x²²Z) k IS Conservative, hence…

A:

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

A:

Q: Find the work done by the force F 6xy i + line segments from (-4, 4) to (0, 0) and from (0, 0) to…

A: Consider  F(x,y)=M(x,y)i+N(x,y)j is vector valued function then : if ∂M∂y=∂N∂x then F is called to…

Q: Calculate the work done by the force F(x, y) = y?î+ xyj in moving a particle along the line which…

A:

Q: Q6/ A boxful has been moved a distance (2m) in a F = 5.2 i+ 3J horizontal direction due to effect of…

A: Work done by a force is equal to the product of Force applied in the direction of distance and…

Q: What would be the resultant force F of the triangular distributed load and its location 'd' measured…

A: Given,

Q: Suppose that 5 J of work is needed to stretch a spring from its natural length of 24 cm to a length…

A: Let the force to hold the spring at a distance x beyond the natural length x is = f(x)=kx For 40 cm,…

Q: Find the work done by the force F =xyi + (y - x)j over the straight line from (- 2, - 1) to (-1,0).

A:

Q: F= (e* – y+ xcosh(x))i+ (y³/2 + x)j.

A:

Q: 6. Find the work done by the force F = 31 – 5j in moving an object from the point (2, 2) to the…

A: Given that the force F=3i-5j moving from the point (2,2) to the point (7,-13). We need to find the…

Q: Compute the work done by the force along the curve (use defini- tion): 1 F = [3r – y + y] curve is…

A:

Q: Find the gradient of f at the indicated point. f(x, y) = 3x² + yt; (4,1) NOTE: Give your answer in…

A:

Q: A particle of mass, m, moves along a straight line while subject to (1) a force proportional to its…

A:

Q: 4. Find the work done by the force F = (ry, y – x) when moved counterclockwise along the circle of…

A:

Q: In what direction from the point (1,-1) is the instantaneous rate of change of 22 f(x,y) = 3x* –…

A:

Q: Find the work done by the force F= xyi + (y - x)j over the straight line from (1,2) to (3,6).

A: we have to find the work done by the given force

Q: A force F(x) = 10−2x N applied in the positive x-direction moves an object 3m from x = 2to x = 5.…

A: Given that , Fx=10-2x N Work (W)=?

Q: Find the work done by the force F = xy i + ( y - x)j over the straight line from (1, 1) to (2, 3).

A:

Q: The work done by the force F = in the displacement along the path C: r(t)=from the point (1,0,0) to…

A: To find the work done by a force

Q: When a particle of mass m is at (x, 0), it is attracted toward the origin with a force whose…

A: Given: When a particle of mass m is at (x, 0), it is attracted toward the origin with a force whose…

Q: Find the work done for a force F = N from x =2 to x =3 m. x2

A:

Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

A:

Q: Find the work done when a constant force F=16l bs moves a chair from x =2.4 to x =3.1 ft. along the…

A: Solve the following

Q: Suppose that an object moves in the positive direction along a coordinate line while subjected to a…

A: Using formula for work done

Q: Find the work done by the force F (x; y) = xyi-(y-x)j over the straight line from (1,1) to (2,3)

A:

Q: Suppose that an object moves in the positive direction along a coordinate line over the interval [a,…

A: Let the object moves in the positive direction along a coordinate line over the interval [a, b] Let…

Q: Find the work done by the force F= xyi + (y - x)j over the straight line from (-1,- 2) to (2,1).

A:

Q: 4. Find the work done by the force F(r,y,2) = (x,-z,2y) in moving straight from (0,0,0) to (1.1.0),…

A:

Q: Q7) The work done by the force F = 2j to move a particle from the origin to the point (3,3,3) is:

A:

Q: Find the work done by the force F = 4xyỉ + (2x2 - 3xy)j by pushing a particle along the line segment…

A: Step:-1 Given Force is F→ =4xy i→ +2x2 -3xy j→ Here, given that particle moves along the line…

Q: Determine the force being experienced by a 2-microcoulomb charge at (-2,4,6) m due to another point…

A:

Q: Consider a beam of length 10m and negligible mass, modelled as a rigid body in the x-direction from…

A: Here I am attaching image so that you understand each and every step.

Q: Find the work done for a force F 36 N from x =2 to x =6 m. %3D

A: Here we have to find the work done by the given force on the given interval. Here we use integration…

Q: Find the work done if a force of F-4i + 7j Newtons moves an object from point A(-9,0) to the point…

A: Here we have to find the work done. The solution is following.

Q: How much work is required to move an object from x = 1 to x = 3 (measured in meters) in the presence…

A: The function f(x)=2x2. N moves an object from x = 1 to x = 3. We have to find work required to move…

Q: Find the work done by the force F(x, y, z) = (x, —z, 2y) in moving straight from (0,0,0) to (1,1,0),…

A:

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: