Find the length of the curve, L. y? = 16 (z+ 3),0sIs1. y > 0

Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0≤t≤2

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Q: Find the exact length of the curve. x = 6 + 3t, y = 9 + 2r, 0sts 5

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Q: Find the exact length of the curve. y? = 16(x + 4)3, Osxs 2, y > 0

A: Given data:   The given expression is y2=16(x+4)3. Th given limits of x is [a,b] =[0,2].   The given…

Q: Find the exact length of the curve x = 5 + 12t? for 0 <t <1 y = 6 + 8t3

A: The objective is to find the exact length of the curve x=5+12t2, y=6+8t3 for 0≤t≤1 Now, dxdt=24t and…

Q: Find the exact length of the curve. x = 9 + 6t2, y = 4 + 4t3,

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Q: x = 12t°, y = 18t², 0 sts v8 X= The length of the curve x = 12t°, y = 18t on 0sts V8 is

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Q: Find the exact length of the curve. x = 7 + 12t, y = 5 + 8t, 0sts 4

A: Given :      x=7+12t2 ,y=5+8t3 ,  0≤t≤4

Q: Find the length of the curve x = 1+ 3t2, y= 4+ 2t³, 0 <t< 1. Length =

A: Given curve x=1+3t2,   y=4+2t3       0≤t≤1

Q: Find the exact length of the curve given by 2t2 t3 (0 <t < 5). x = Length = ||

A: Solve for the length of curve

Q: Find the lengthof the curve 」 9メ d S16 3_ %3D

A: Given curve is By fundamental theorem of calculus,

Q: Find the exact length of the curve. y? = 64(x + 5)3, 0sxs1, y > 0

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Q: Find the length of the curve. x = 4t, y =- 3/2,0st s9 0 st 122 3

A: Arc length of the given curve

Q: tind the point on the curve y=Jx that is closest to the point (3,0).

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Q: Find the exact length of the curve. x = 8 + 9t?, y = 3 + 6t, 0 sts4

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Q: Find the exact length of the curve. x = 1 + 9t2, y = 8 + 6t, 0 sts 4

A: Answer is mentioned below

Q: Find the length of the curve, L. y = 16 (a + 3)", 0s s1. y> 0

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Q: Find the exact length of the curve x = tsint, y = t cost where 0 ≤ t ≤ 1.

A: answer is in next step

Q: Find the exact length of the curve. y = x3/2, osxs 6 3

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Q: Find the length of the curve. y = 2 – 4x, 1<a< 3 O 54 3V17 O 17 O 2y17

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Q: e length of the curve y = V 4 – x2, 0 <x< 2. ing the shape of the curve.

A: Use the arc length formula to find the length of the curve.  y=(4-x2)1/2 , 0&lt;=x&lt;=2

Q: Find the exact length of the curve for the parametric equation

A: Let's say the length of the curve is L.  0 ≤ t ≤ 1 Hence, the desired length will be calculated as:

Q: Find the exact length of the curve. x = 2 + 3t2, y = 5 + 2t3, 0sts 2

A: Given,

Q: Find the exact length of the curve. x = 6 + 3t?, y = 2 + 2t3, 0 sts 5

A:

Q: Find the length of the curve.y=x3+14x,1≤x≤2. Round the approximation to 4 decimal places.

A: The length of the arc from point a to b is given by:

Q: Find the exact length of the curve. x = 8 + 12t2, y = 9 + 8t³, 0 st< 3

A: given parametric equation of curvex = 8+12t2 ,   y = a+8t3

Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: Find the length of the curve. 5 17) y = 3x3/2 from x = 0 to x =- 335 335 B) 162 335 A) 243 D) 1 3

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Q: C3. Find the length of the of the curve x= 1 from y = 1 to y = 2 %3D 4 8y?

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Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

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Q: Find the exact length of the curve. x = 1 + 3t2, y = 9 + 2t, 0sts 4

A:

Q: Find the length of the curve r= e2θ, 0≤θ≤2

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Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: Find the length of the curve x = 3t2 + 10, y=2t3+ 11, O<t<1.

A: Given,         The length of the curve x=3t2+10 , y=2t3+11 , 0≤t≤1We know that,         The length…

Q: Find the exact length of the curve. 36y =(x+4). 5 5 x s 6, y 20

A: Given: 36y2=(x2-4)3,  5≤x≤6,  y≥0 Arc length of curve y=f(x) on [a, b] can be calculated by…

Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

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Q: Find the exact length of the curve given by a = t° ,y (0 <t< 4). Length =

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Q: Find the length of the curve. 6t, , r(t) 0 <t< 1

A: Given:-r(t)=6t, t2, 19t3,         0≤t≤1since we have to find the length of curve.

Q: Find the length of the curve. x = (v - 1) 3/2 from y = 16 to y = 25 O 4 61 O IK

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Q: Find the exact length of the curve. 1 Vy (v - 3), 4 < y< 16 3 X =

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Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0 sts 4

A: We find dx/dt and dy/dt

Q: Find

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Q: Find the exact length of the curve. x = et + e=t, y = 5 – 2t, 0st< 4

A: The solution are next step

Q: What is the length of the curve I= cost +tsint, y=sint - tcost, (0 <t< 2n) ?

A:

Q: Find the length of the curve, L. y² = 64 (x + 1)° , 0 0 L =

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Q: Find the exact length of the curve. X = 4 + 6t2, y = 8 + 4t3, 0sts 2

A:

Q: 2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

A:

Q: Find the exact length of the curve. x = 1 + 12t2, y = 4 + 8t3, 0 sts 3

A:

Q: Find the exact length of the curve. x = 1 + 9t, y = 8 + 6t, 0sts 3

A: Explanation of the answer is as follows

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.