Consider Vector field given by A = pcos(@)a,+ ag, the line integral of VectorA 3 over the segment 2 equals to.. Y4 2) 0. 2

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

A:

Q: Consider the vector field F = . Find the line integral F. dr, where C is the portion of the curve y…

A:

Q: A force F = -3i +j+6k acts through the point (5,-2,-1). Find its moment about the point (3,0,2).

A: Moment of force about the point is given by cross product of position vector r about a point and…

Q: Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the…

A: v→=y2i→+1.3x2j→ Initial point 1,2 ∆t=0.1

Q: Define Vector Line Integral.

A: A line integral is the integral of some function along a curve. One can integrate a scalar-valued…

Q: H=pz Csup ap te'sin dg tpan 2 At point (1, ,6)

A:

Q: Find the electric flux PE across the part of the cylinder x² + y² = 9,0 ≤ z ≤ 2, in the direction of…

A: Given information:The electric field is given as .The surface is a part of the cylinder defined by…

Q: :::.. V : 5+j wi +4j Find the specific Scalar .(.. )

A:

Q: Find the curl of the vector field F = <yx³, xz³, zy² curl F = i + k + V

A: For the given field F=yx5, xz3, zy2, we need to calculate the curl. This can be evaluated as…

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and…

A: Solution: The objective is to find a vector tangent to the curve of intersection of the two…

Q: Given the general vector A=(sin20) a_ find the curl of A at (2,π/4,0) O-0.5a_z 0.5 a_ - a_p 2a_z

A:

Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to $(r) : equi-…

A: The formula to calculate the vector which is normal to the equipotential  line of the potential…

Q: (9) Let F Be a vector field over ø be a scalar field. Prove the following similarity: V. (OF) = (Vo)…

A:

Q: The acceleration of a particle at any time >=0 is given by: dr a = == (25cos2t)i + (16sen2t)j +…

A:

Q: a 3d vector field given by V=5xyi+5yj-4zk represents the flow of water out of a system. use gausses…

A:

Q: Apply fundamental theorem for conservative vector field to find the line integral fF dr where F =…

A:

Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt. n'=dxn, h' = d x b and…

A:

Q: Calculate the flux of the vector field (³, ³), out of the annular region between the x² + y² = 9 and…

A:

Q: Find a Vector ū: non zero Vector perpendicular to the

A:

Q: For the scalar function f, div(grad f) is equal to Select one: a. + + dx?' ay? ' az? b. dx dy dz C.…

A:

Q: Two points in rectangular coordinates are given by P₁ (0,0,2) and P₂ (0,1, √3). Obtain the line…

A: We are given points in rectangular coordinates are given by P1(0, 0, 2) and P20, 1, 3. Here, we need…

Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly hree Os, five 1s,…

A: Strings of 12 ternary digits, 3 possibilities for each digit in the string, gives a total of 3^12 =…

Q: 2 Locate the numbers z₁+z₂ and z, - z₂ vectorially when z₁ = 2i, z₂ ==-i. 3

A: Use addition the evaluate these numbers then plot it

Q: Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N is a vector…

A:

Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

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: