Find the arc length (s) of the curve 7 (t) = (12 sin(5t), 2/11 cos(5t), 10 cos(5t)) for 0

Q: Find the point on the curve r(t) (12 sin t)i – (12 cos t)j + 9tk at a distance a) 5n units and b)…

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Q: Find the arclength of the curve z 9 cos(9t), y = 9 sin(9t) with 0 <t< 36

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

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Q: Find the arc length (s) of the curve r(t) = (cos(3t), 5t, sin(3t)) for 1 <t < 5

A: r(t)⇀={cos(3t),5t,sin(3t)}Now we can evaluate that x(t)=cos(3t)y(t)=5tz(t)=sin(3t) We know that the…

Q: Find the arc length of the curve y = x² from x = 0 to x = 1.

A: Given: y=x2, x∈0,1 We know that for any given curvey=fx on intervala,b, arc lengthL is given by…

Q: (). (a) Find the arc length function for the curve y = In(sin(x)), 0 < x < T, with starting point…

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Q: d the arc length of the curve y=(x^2)/2 - (lnx)/4 O

A: Explanation and solution is given below....

Q: 2:(b) Find the exact arc length of the curve x=e"(sint+ cost), y=e" (sint – cost) over the interval…

A: Given

Q: Find the arc length (s) of the curve 7(t) = (4 cos( – 4t), 2/5 cos( – 4t), 6 sin( – 4t)) for 0 <t <…

A: Given that  The curve is  To find the arc length of the curve

Q: (b) Calculate the arc length of the curve y from x = 1 and x = 2. +

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Q: I need to solve this question

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Q: calculate the arc length over the given interval y = 14x2 − 1/2 ln x, [1, 2e]

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Q: find the arc length of the curve y=In(sec x) from x=0 to x=pi/3

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Q: Find the arc length function for the curve y = sin+(x) V1-x² with starting point (0, 1).

A: As we know that; The expression for the length of arc of the curve is: L=∫ab1+dydx2dx The Power…

Q: If the arc length s of the curve C:r (t) = cos(t)i + sin(t)j+2tk from t = 0 to t = b is 20 units,…

A: The arc length of a parametric curve defined by the vector r→=f(t), g(t), h(t) defined over the…

Q: Find the arc length (s) of the curve r(t) = (2t, 4 cos(3t), 4 sin(3t)) for 1 <t < 4 S =

A: Application of integration and partial derivatives use to solve this problem.

Q: Find the arc length of the curve r(t) = (2t3/2, cos 2t, sin 2t) from t = 0 to t = 1. %3D

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Q: Find the exact arc length of the graph of y==x² -- In(x) where xe[1, 2e].

A: Given : f(x)=14x2−12lnx    on  x∈[1,2e]

Q: Find the arc length of the curve Nephroid perimeter: x = a(3 cos t − cos 3t) ,   y = a(3 sin t − sin…

A: Given: x=a(3cost−cos3t)y=a(3sint−sin3t)0≤x≤2

Q: Find the arc length s of the curve y= x2 on the interval  [0,2]

A: The objective of the question is determine the arc length of the given function.

Q: Find the arc length function for the curve y = sin+(x) + V1- x² with starting point (0, 1). s(x) =

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

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Q: Find the arclength of the curve x= 4cos(6t), y= 4sin(6t) with 0 less than or equal to t less than or…

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Q: 2. Find the arc length of the curve y= from x-2 to xD3 16 2x2

A: The solution is given as

Q: 2. Sketch and find the arc length of the curve below. 3 x = cos* t, y = sin³ t

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Q: Calculate the arc length of y = 9x + 1 as x varies from 0 to 5. S -

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Q: -Find the arc length of the curve: y3 x2 where 1<x<4

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Q: 9. Find the arc length of the curve 24xy = x* + 48 from x = 2 to x 4.

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Q: Calculate the arc length of the curve y over the given interval. y = In(cos x), 0 < x <T/4,

A: Over the interval a ≤ x ≤ b.

Q: Find the arc length of the curve y In(cosa) from = 0 to 2/4.

A:

Q: What is the arc length of the curve x = (1/2)y2 - (1/4)ln y from y = 1 to y = e?

A: Here, we have given x is a function of y. So, we will use the following formula for finding the arc…

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

A: Given,

Q: Find the arc length of the curve y = (ex + e-x)/(2), 0 ≤ x ≤ 2.

A:

Q: 3. Find the arc length of the curve 24xy y+ 48 from y-2 to y-4 1 to from

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Q: 7. Find the arc length of the following plane curve: x = e' (sint + cos t), y = e' (cost – sin t),…

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Q: Find the arc length of the following curve on the given interval. y = 1/2(e^x+e^-x) [ln2,…

A: Find  the  arc  length  of  the following  curve  on  the given interval. y = 1/2(e^x+e^-x) [ln2,…

Q: Use parametric-form integration to find the Arc Length of the arc x=(1/3)t^3 defined by y=(1/2)t^2…

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Q: Find the arc length of the graph of the function over the interval. y = In(sin z);

A: Given,          y=lnsinx ; π4,3π4

Q: 9) Find the exact (arc) length of the curve. x = 2t – sin(2t), y = 1 – cos(2t), 0<t<r. -

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Q: Find the length of the arc from 0 = 0 to 0 = 2n for the cardioid r = f (0) = 2 – 2 cos 0.

A: Solution if r=fθ  has a continuous first derivativefor α≤θ≤β then length of polar…

Q: 2. Find the arc length of the curve y = 16 from x=2 to x-3 2x

A: Given y=x416+12x2, x=2 to x=3

Q: Find the arc length of y=sin(πx) on [0,2]

A: Find the length of the arc: y=sinπxInterval =0,2dydx=πcosπxarc length=∫ab1+dydx2dx  = ∫021+πcosπx2dx…

Q: Find the arclength of the curve z = 7 cos(3t), y = 7 sin(3t) with 0 < t< 12

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

A:

Q: Find the arc length of the curve .x = ln(sec t + tan t) - sin t  y = cost, 0 ≤ t ≤ π/3

A:

Q: b) y = ln (cos x) 0 <x<- 3

A: Given: y=ln(cosx) in the interval 0≤x≤π3

Q: Find the exact arc length of the curve x = e2" (sin t – cos t),y= e2t(sin t + cos t) (-1<t< 1).

A:

Q: Find the arc length of the curve 7(t) = (2t/2, cos 2t , sin 2t) for 0<t <1

A: Differentiate f(t), g(t) and h(t) with respect to t, to obtain the tangent vector r→'t. rt=2t32,…

Q: Find the arc length of the curve y = In(cos x),0 < x <. 3

A: Arc length of a curve y=f(x) for a≤x≤b is given by L=∫ab1+f'(x)2 dx

Q: Find the arc length of the curve x = cos 2t, y = sin 2t, 0 < t < 5 27 -2T

A: The arc length of the curve x=cos2t, y=sin2t, 0≤t≤π2

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.