Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

Q: Find the directional derivative of f(x,y)=yln(x+y) at the point (-3,5) in the direction of the…

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Q: Find the diectional derivative of the function f (xiy,z)= sin (xy+2) at the point of P(1, al2 x4) a…

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Q: f(x, 3) = In(x? + Y²òf function P(3,4) at the point of i = (9, 12) Directional derivative in the…

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Q: Let R be a differentiable vector-valued function such that R'(t) = (3t2, 2tvt2 + 1, 2t + 3) and R(1)…

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Q: A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at time t…

A: Given: A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at…

Q: Find the directional derivative of f(x, y) = /xy at the point P = (2,8) in the direction of the…

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Q: Suppose that f(x, y) = x³y². Find the directional derivative of f(x, y) in the direction of (-3, 1)…

A: Given that the vector fieldfx,y=x3y2 The directional vector u→=-3,1The point  -2,2    .

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: