The arc length of the portion of the curve y=x² with 0

Q: Calculate the arc length of y = ((72x)/2 – (72x)2) over the interval [2,8].

A: For Y=F(x) , a≤x≤blength of the curve = ∫ab1+dydx2 , dx                        or                arc…

Q: Find the arc length of the catenary y = coshx between x 0 and x = In4.

A: we'll allow providing one solution at a time. Please submit the rest questions separately.   Given:…

Q: find the arc length of the curve on the indicated interval of the parameter x=4t+9 y=9t-5 o<t<2

A: The arc length of a parametric curve can be found by the formula, L=∫titfdxdt2+dydt2dt consider the…

Q: What is the arc length of the curve y = (2/3)(x-4)3/2 from the point where x = 4 to the point where…

A: Given: y=23(x-4)32

Q: 1. Find the length of arc of the curve y = () from the point where x = to the point where x = 2.

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: Approximate the arc length of the curve y=1/4x4 over the interval [1,2] using the trapezoidal rule…

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Q: Find the length of arc XY

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Q: Find the arc length of the curve y=ln (secx) from x=0 to x=(pi )/(3)

A: Use formula

Q: Find the arc length of the curve x = -2y³/2 from y = 0 to y = 10. Length =

A: The given curve is x=-2y32 from y=0 to y=10. Find the arc length. As we know the formula of arc…

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

A: given curve     x=2y            we have to   find the arch length fro (0,0)  to  (4,4)now  x=2y ⇒…

Q: Find the length of the arc of the curve y = In x over the interval: [1, 5. Round the answer to four…

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Q: The arc length function of the curve y = 2 In x taking the point Po(1, –) 4 as a starting point is

A: see 2nd step

Q: Find the length of the arc of the curve y=lnx over the interval: [1,6]. Round the answer to four…

A: The formula for the arc length of the curve is L=∫ab1+dydx2 dx  or  ∫cd1+dxdy2  dy Here, the given…

Q: Determine the the length of the arc of the curve for the given interval. y=sqrt(x+2). 1 ≤x<7. Answer…

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Q: Find the arc length function for the curve y=  sin inverse x  + sqrt ( 1 - x sq. ) with starting…

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Q: 2 Find the arc length for y = 3x3 on [1, 8]

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Q: Find the arc length of the graph of the function over the indicated interval. y = 3, [64, 125]

A: The arc length of curve f between the points a and b is given by s=∫ab1+f'x2dx.

Q: The arc length of the portion of the curve y = e with 3 <x<5 is None OA. sz128.35 В. sz15.54…

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Q: Find the arc length of the curve x -3y3/2 from y = 0 to y = 10. Length

A: Integration √1+(f'(y)) 2dy

Q: Find the arc length of the catenary y = coshx between x = 0 and x = ln4.

A: Given: y = coshx between x = 0 and x = ln4.

Q: Find the arc length of the graph of the function y = ln(1 − x2 ) on the interval 0 ≤ x ≤ 1/2

A: Given:            y= ln 1-x2,  0≤x≤12    Formula to be used: Let y=f(x) be differentiable function…

Q: Find the arc length of the graph of the function over the indicated interval. x= =cy² + 2)3/2, 0sys2

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Q: Find the length of the arc of the curve y=x+3 from the point where y=2 to the point where y=x^2+1…

A: y=x+3  ⇒x=y-3⇒dx=dy⇒dxdy=1 The formula for the length of the arc from the point y=2 to y=x2+1…

Q: Find the arc length of the graph of the function over the indicated interval.

A: Differentiating with respect to x, we get

Q: Find the arc length of the catenary y = cosh x between x = 0and x = ln 2.

A: Given y=cosh(x)

Q: Find the arc length function for the curve y = 2x3/2 starting at the point (1,2). %3D

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Q: Find the arc length of the curve y= 7x+4 On the interval 3

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Q: Find the arc length of the graph of y = -- 2 over (0,4].

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: Find the length of arc of the curve y =÷(x² + 2)3/2 from the point where x = 0 to the point where x…

A: Consider the given curve: fx=13x2+232Interval  0≤x≤3Differentiate w.r.t.…

Q: Find the arc length of the curve y = log(1/cosx) from x = (/4) tox= (/3)

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Q: 3. Find the length of arc of the curve y = ln(secx) from x = 0 to x = 4

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Q: Find the arc length of y = ²√x(3-x) for 0 ≤ x ≤ 3. - Express your answer in decimal form rounded…

A: Given problem:- Find the arc length of y = (1/3)√x(3-x) for 0 ≤ x ≤ 3.

Q: Find  the Arc length of the graph of y=Ln(cosx) from x=0 to x=π/4

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: Find the length of the arc y = 8. 1 from X = 1 to x = 4. 4x www

A: Given

Q: Find the exact arc length of the curve over the stated interval. = 3x3/2 – 2, from x = 0 to x = 1…

A: We have to find the arc length of the curve over the stated interval.…

Q: Find the arc length of the segment of curve y = In(cos x) for 0< x<"/3. DO NOT integrate in your…

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Q: Determine the length of the arc x=ln y−(y^2)/8 for 1≤y≤2.

A: The solution are next step

Q: Find the arc length of y= x2/8 - ln(x) from x=1 to x=4

A: We find dy/dx of the given function.

Q: Find the arc length from x=0 to x=100 of the catenary: 150cosh(x/150)

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Q: Find the arc length of the graph of the function over the indicated interval. 3/2 x2 + 1 y = y

A: Here we need to find arc length of y from x=0 to x=1

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8…

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Q: Compute the arc length exactly. Please round your final answer to three decimal places. 1 y = -x -In…

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

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: Find the length of the arc of the curve y = (1 + x²) fron the point where x = 0 to the point where x…

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Q: find the arc length of the curve (1/36)x^6+(3/8)x^−4 from x=1 to x=4 Integral? Arc Length?

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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.