Evaluate the line integral F. dr, where C is given by the vector function r(t). Jc F(x, y) = xy i + 6y2 j r(t) = 16t6 i + tj, 0sts 1 The value of this line integral (and it is a whole number) equals

Q: I Verity Green's F (8,y) = Cx-xy) and the part D={Cs,x) F": theorem for the vector fiela

A: Introduction: Green's theorem connects a line integral around a simple closed curve C to a double…

Q: Evaluate the line integral F• dr, where C is given by the vector functio Jc F(x, y, z) = sin(x) i +…

A:

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

A:

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

A: Given as

Q: Evaluate the line integral, where C is the given curve. xevZ ds, C is the line segment from (0, 0,…

A: Consider the  line integral ∫Cxeyzds Where C is the line segment from (0,0,0) to (3,4,2).

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

A:

Q: Evaluate the line integral F. dr, where C is given by the vector function r(t). C F(x, y, z) = 6zi +…

A: Let's evaluate given integral.

Q: Evaluate the line integral f. 3x?yz ds along C:x = t,y = t²,z = ÷t³ , 0 <t<1

A: Use the following formulae, to obtain the solution.…

Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z over the curve c(t) = (e',…

A:

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

A: Line integration by parameterization

Q: Evaluate the line integral, where C is the given curve. 1 ,C:x =t*, y = t", sis1

A:

Q: Evaluate the line integral, where C is the given space curve.                  ∫C  x2 y ds     C: x=…

A: Since you have sent multiple questions we can just answer one of them because of our company…

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

A:

Q: Evaluate the line integral along the curve C. J (3x - 2y) ds; C is the line segment r(t) = (2t,t)…

A:

Q: Evaluate the line integral, where C is the given space curve.     Cxyeyz dy,   C: x = 4t,  y = 4t2,…

A: Firstly change the given line integral in terms of 't' and then solve.

Q: Evaluate fc F • dr, where F = (z, y2, x) and C is parametrized (in the positive direction) by r(t) =…

A: F=z,y2,x and C is the parametrized by r(t)=t+1,et,t2 for 0&lt;t&lt;2. We have to evaluate ∫CF·dr.

Q: Evaluate the line integral, where C is the given curve. xyeYZ dy, C:x 2t, y = 3t2, z = 3t, osts1 %3D

A:

Q: Evaluate the line integral f, F . dr, where C is the curve given by F(t) = 3 cos ti+ 3 sin t j, 0<t<…

A:

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

A: Given that the function Fx,y,z=x+yi+y-zj+z2k and rt=t2i+t3j+t2k,0≤t≤1. It is required to evaluate…

Q: Evaluate the line integral S, y ds where C:x = t²,y= 2t, 0 <t < 3

A:

Q: Use Green's Theorem to compute the circulation line integral of F(x, y) = (x² – 6y², 5x) over the…

A:

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

A:

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

A: Given  Fx,y,z=x+y2i+xzj+y+zk.. . . . . .1rt=t2i+t3j-2tk . . . . .2and 0≤t≤2 Differentiate (2)…

Q: Given the function f (x, y) = 2?y - tan-(xy) Itan-(ay) %3D Find the vector normal to the level curve…

A: Find the normal vector to the level curve at a point

Q: If = 2xyz?, vector F = xyi - zj + x²k and C is the curve: x = t2, y = 2t, z = t3 from t = 0 to t = 1…

A:

Q: Evaluate the line integral, where C is the given curve. хуеу2 dy, C: х %3D 3t, у%3D 2t?, = 2t3, 0st<…

A: x=3t, y=2t2,z=2t3

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

A:

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

A:

Q: Evaluate the line integral F. dr, where C is given by the vector function r(t). F(x, y) = xyi + 6y?j…

A:

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

A:

Q: Evaluate the surface integral [[ (a² + y²) dS where S is the surface with vector function r(u, v) =…

A:

Q: Evaluate the line integral F. dr, where C is given by the vector function r(t). F(x, y) = xy i + 9y2…

A: Solution

Q: Evaluate an area of a surface where the vector that is normal to the surface is defined as; d. Q =…

A:

Q: Evaluate the line integral ∫F⋅dr, where F(x,y,z)=5xi−yj+zk and C is given by the vector function…

A:

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

A:

Q: Calculate the line integral of the vector-function F(x, y, z) = (y² +2²) i-yzj + xk along the path…

A:

Q: Find the value of the integral of the line ∫CF*dr where C is defined by the vector function r (t)…

A:

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

A: We have given

Q: Calculate the line integral a) |y ds, C:x =ť², y = 2t, 0 <t < 3 C

A: Use parametric to solve

Q: Evaluate the line integral F*dr, where F(x,y,z) = (3sin(x), -4cos(y), 4xz) and C is given by the…

A: Find your answer below

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

A:

Q: por la función vectorial r(t) = cost i+ sen tj+t k, #/4 stSn/2. 10p

A:

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

A:

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

A:

Q: Calculate the integral J, VX (y1).ri de if i is the outward normal unit vector of an ellipsoidal…

A:

Q: Find the flux of F across S, F.N ds where N is the upward unit normal vector to S. F(x, y, z) = -2i…

A:

Q: Q3 Evaluate Curlvoñ, where v = 2.xyi +(x² – 2 y)j + xzk and i is a unit vector normal to the surface…

A:

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

A:

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

A: Formula Used:

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: