Find the exact arc length of the curve over the interval 24xy = y* + 48 from y = 2 to y = 4 . Eind the surface area of the region under the curve

Q: Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the…

A: Given,  y=xe-x+9

Q: Find the area of the surface obtained by rotating the given curve about the x-axis. - 10 10 cos (0),…

A: Find the derivatives with respect to θ

Q: Set up a (sum of) definite integral(s) that is equal to the arc length of the portion of the curve y…

A: The length of the curve y=f(x) between the limits x=a to x=b is given by; L=∫ab1+dydx2dx

Q: Find the area of the surface swept out by revolving the para- metric curve x = 5 cost + 5t sin t y =…

A: Area under curve.

Q: ) Find the arc length of the curve x = cost + tsint, y = sint – tcost on the given interval 0 < t <…

A: Here we have to find the arc length of the curve x=cost+tsint, y=sint-tcost, on the given interval…

Q: arc length of y = e,0 << 2

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Q: Calculate the arc length integral s for the logarithmic spiral c(t) = (e' cos(t), e sin(t)) for 0…

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Q: Express the arc length of the curve y = x 4 between x = 2 and x = 6as an integral (but do not…

A: Given y=x4 between x=2 and x=6

Q: Find the arc length of the curve y = ln(x) for 1 <I<e. ||

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Q: Calculate the arc length of x = 6t2,y = 6t – 2t³ from 0 to 4

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Q: Express the arc length of the curve y = tan x for O &lt; x &lt; ~ as anintegral (but do not…

A: Given that, Curve, y=tanx 0&lt;x&lt;∞

Q: Find the arc length of the portion of the graph of y=x2+x , where −1≤x≤1 You may numerically…

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Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: T X =…

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Q: Find the surface area generated when the arc given by y = 2/15 – x; 0 <x < 15, is revolved about the…

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Q: Find the area of the surface obtained by revolving the given curve about the x-axis. on (0, In(3)

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Q: (a) Set up an integral for the length of the arc of the hyperbola xy = 1 from the point (1,1)  to…

A: Part (a)

Q: Find the surface area of a sphere of radius r using the formula of arc length with respect to x.

A: The objective is to find the surface area of a sphere of radius r using the formula of arc length…

Q: Calculate the arc length of y = x² – In(x) over the interval [1, 6e]. (Use decimal notation. Give…

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Q: Compute the trapezoidal approximation T5 to the arc length s of y = tan x over [0, 4].

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Q: Find the arc length of f (x) = In|sec x| over [a/6, x/3]. Round your answer to two decimal places.

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Q: Express the arc length of the curve y = tan (x) for < x < as an integral (but do not evaluate).…

A: length of the carve over the intervel a to b is       ∫ab1+(dydx)2 Where y is the function…

Q: Find the point on the curve r(t)=(5sint)i+(−5cost)j−12tk at a distance 13π units along the curve…

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Q: Find the point On the curve R(t) = 5sint i + 5cost j + 12t at adistance (267) units along the curve…

A: Given:-               rt = 5 sin t, 5 cos t, 12 tdistance = 26 π unitspoint = 0,0,0

Q: 5) Determine the area of the surface obtained by rotating the arc y = Vx –1 around the x- axis from…

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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: Which integral gives the arc length of the curve over the interval from t = a to t = b?

A: This is a problem related to integration. Based on the general formula of length of arc we will…

Q: Find the area of the surface generated when the indicated arc is revolved about the y-axis. y=x^2…

A: The given equation is y=x2 from x=0 to x=1. Find the area of the surface generated when the…

Q: Find the area of the surface generated by revolving the given curve about the indicated axis. 1. x =…

A: Consider two parametric equations and with . Then the area of the surface obtained by rotating…

Q: Find the area of the surface generated by revolving about the y-axis the arc C given by C = { (x,y)…

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Q: Find the arc length of f(x) = In(csc(x)) on [0, T/4]. CSC

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Q: Find the arc length of curve represented by X=cost+tsint   , y=sint-tcost               (0≤t≤π)

A: We know that: if parametric equation of a curve x=f(t) and y=g(t) is bounded by the region a≤t≤b,…

Q: Approximate the arc length to three decimal places given: y = In(cos x) , [0,÷]

A: Given curve is Differentiating with respect to x, we get

Q: Find the area of the surface obtained by rotating the given curve about x-axis. x=cos (t),…

A: We have to find the area of the surface obtained by rotating the given curve about the x-axis. x=cos…

Q: Find the area of the surface generated when the given arc is revolved about the y-axis ㄷ y = 4 - x²…

A: We have to find area of the surface .

Q: Consider the curve x = VT(y – 3)/3. Find the arc length of this curve over the interval 1 <y <9.

A: According to the given information, it is required to find the arc length of the curve over the…

Q: The area bounded by the ourves y= *", and y=2x iş revolved about the y-axis, Find the moment of…

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Q: Set up, but DO NOT EVALUATE, an integral for the length of the curve y = e-2? for arc length = | dx

A: L = ∫ab1+dydx2 dx

Q: Find the exact arc length of the curve 2xy = y² + 4 over the interval 2 ≤ y ≤ 4. Find the area of…

A: Given: 2xy=y2+4 over 2≤y≤4 to find the arc length of the curve and given the another equation is…

Q: Express the arc length of the curve y = tan (x) for as an integral (but do not evaluate). Choose the…

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Q: Show that, for any interval, the arc length of y = }e² +e¬# is equal to the area under that portion…

A: Consider the given equation, y=14ex+e-x   The formula of arc length is defined as, Arc…

Q: find the area of the surface formed by revolving the cardioid r= a(1+cosθ) about the x-axis

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Q: Find the area of the surface generated by revolving the curve x = Vy, over the interval 8 sys 27…

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Q: r(t) = (e' cos t)i + (e' sin t)j + e'k, -In 4 < t< 0

A: rt=et cost i+et sint j+et k,   -ln4≤t≤0 Differentiating with respect to t, we get vt=drtdt=ddtet…

Q: Find the area of the surface generated when the indicated arc is revolved about the y -axis. 6. y =…

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Q: b) Sketch the graph and find the points on the cardioid r=a(1+cos) at which tangent lines are…

A: Consider the equation of the cardioid, r=a1+cosθ The graph will be,

Q: y = Vx for 0<x < 3.

A: the given function is: y=x for 0≤x≤3 we have to determine the length of the curve.   as we know that…

Q: The integral V1 + ešx dx represents the arc length of which curve (for 0<x<1) ?

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Q: Set up but do not compute the integral for the arc length of the curve y = e-*,-1<x<1

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Q: Find the arc length of the curve Cycloid arch: x = a(θ − sin θ), y = a(1 − cos θ) , on the interval…

A: Cycloid arch: x = a(θ − sin θ), y = a(1 − cos θ)  interval [0, 2 ].

Q: Prove that the arc length on any interval has the same value as the area under the curve.

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