Find the length L of the curve R(t) = 4 cos(5t) i – 4sin(5t) j + tk over the interval [3, 6]. L = 3sqrt(416)

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Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

Q: Compute the length of the curve over the given interval. r(t) =〈2t, ln t,t^2〉, 1 ≤ t ≤ 4

A: it is known that the length of the curve can be calcualted by the integral formula…

Q: 1. Consider the curve C: r(t) = (t - sin t)i + (1– cos t)j, 0StS 2. %3| | (a) Find an equation of…

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Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 ln cos t k,     0 ≤ t ≤ π/4

A: Consider the length of the curve is, r(t)=costi+sintj+(lncost)k Then,…

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Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: 1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

A: according to the guideline, we are allowed to answer the only the first question  please repost…

Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26p units along the…

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Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0 <t< n/4

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Q: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

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Q: 13. Find the value of t in the given interval at which the given curve is not smooth. r(t)=(5cost-…

A: Given curve: r(t)=5cos t-cos 5t, 5sin t-sin 5tt interval: π4,3π4

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Q: Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y =…

A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: Find the point on the curve r(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13π units along…

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Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

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Q: Find the length of the curve. r(t) : cos(8t) i + sin(8t)j + 8 In(cos(t)) k, 0 stS T/4

A: Solution is given as below:

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Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

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Q: Q3) Compute for y(x) = cos'(4vT)+ 5x and x(t) = 4 at t=1

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Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t) j + 4ln(cos(t)) k,  0 ≤ t ≤ ?/4

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Q: 1. Find the length of the curve r(t) = (sin 2t, cos! cos 2t) from t =0 to t 2n. %3D II

A: 1)- Given: r→t=sin 2t, cos 2t from t=0 to t=2π. The objective is to determine the length of the…

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Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< t/4

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Q: Find the Giniindex for the lorenz curve L (X)= 0.3X + O=7X 11

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Q: Find the maximum, minimum and inflection points of the fur y= 3 sin 2x at [0, T].

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Q: Find the length of the curve 7 (t) = (4 cos(t), 4 sin(t), 3t) for – 1 <t< 4

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Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

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Q: 2. Let y be the curve in R3 given by t (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds

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Q: Find the length L of the curve R(t) = 4ť²i + t° j+ 4k over the interval [3, 6]. L

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Q: a The integral that represents the length of the curve 7 (t) = <2/t,cos (2t3/2), sin (2t3/2)) where…

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Q: Find the length of the curve defined by the following function for 0 <t < 2n. 7(t) = (– cos 2t)i +…

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Q: The x- coordinate of the point on the graph of y = yx – 1 at which the tangent line is perpendicular…

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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Q: Find F. dř for F = 5yi – (sin y)j on the curve counterclockwise around the unit circle C starting at…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.