2. Find the point on the curve r(t) = (12 sin t, -12 cos t, 5t) at a distance 137 units along the curve from the point (0,-12, 0) in the direction opposite to the direction of increasing arc length.

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)…

A:

Q: 4. Use the Arc Length in Parametric Form formula to find the arc length of the curve with the given…

A: Given parametric equations, x= 3sint ,   y=3cost,     0≤t≤π3

Q: Find the exact arc length of the curve over the stated interval. y = 7x/2 – 5, from x = 0 to x = 1 -…

A:

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…

A:

Q: Find the arc length L of the graph of the given equation from P to Q or on the specified interval. y…

A: Solution is written in below steps.

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

A:

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

A:

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

A:

Q: I need to solve this question

A:

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

A:

Q: Find the exact arc length of the curve r = e from 0 = ln 2 to 0 = ln 8.

A:

Q: Consider the parametric curve: x = sin² (t) y = -9t Which integral gives the arc length of the curve…

A:

Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j – 12tk at a distance 65r units along the…

A:

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

A:

Q: Let the curve C be given by r(t) = (cos(3t), t, sin(3t)). %3D (a) Reparametrize the curve with…

A: (a)  Given, r→(t)=cos(3t),t,sin(3t)....................(1) Differentiating,…

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: 2. Find the point on the curve r(1)=(5sint)i-(5cost)j+12tk at a distance 267 units along the curve…

A:

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

A:

Q: 1) Find the arc length of the curve over the interval: | 2 3 (a) [0,3] for f (x) =x X2 (b) for y =…

A:

Q: Find the arc length of the curve: x = 2 sin^-1 (t), y = ln(1 - t^2), over the interval

A:

Q: 7. Find the arc length of each curve (integrate by hand) a) x = -8y– 3 on [– 2,6] b) y = , 3 on…

A: Here we have to find the arc length of the given curves.

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

A:

Q: Find the arclength of the curve over the given interval. (a) r = 1 + sin θ, 0 ≤ θ ≤ 2π

A: Given: The curve is: r=1+sinθ over the interval 0≤θ≤2π The objective is to find the arclength of the…

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

A:

Q: x = 4 sint, y= In(1+t), (-2<t <1).

A:

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

A:

Q: 3 6. Find the arc length of f(x) = G (x2 + 2)z on the interval [0,9]

A:

Q: 10. Find the point on the curve r(t) = (12 sin t)i – (12 cos t)j + 5tk at a distance 13 T units…

A:

Q: Find the point on the curve F(t) - (5 sin t)i + (5 con t)j+ 12tk at a distance 20 units along the…

A: Let's find.

Q: Find the exact arc length of the curve over the stated interval.  x = 1/8 y^4 + 1/4 y^-2, from y =…

A:

Q: Find the exact arc length of the curve x = 3 0² +2) from y = 2 to y = 6. -

A: The arc length L of the curve x=13y2+232 from y=2 , y=6 is given by,                        L=∫26…

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: Consider the parametric curve: X = sin² (t) y = -9t Which integral gives the arc length of the curve…

A: Topic = Integration

Q: Show that the arc length of the graph of y = sin x on the interval [0, 2π] is equal to the…

A: Given, Equation of Ellipse is x2+2y2=2 Now divide the equation of ellipse by "2" we get,…

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

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

Q: Find the arc length of the curve on the given interval x (0) = 0³, y (0) = 0² ; 0 ≤ 0 ≤ 2

A:

Q: Find the arc length of the curves x = e-20 (sine + cos0), y = e-20 (sine – cose) over the interval…

A: Definition used -                    Length of the curve…

Q: Find the arc length of y = 7r +1 over the interval [0, 2]

A: y = 7r + 1 arc length=∫02 1+(dy/dr)2dr dy/dr = 7' arc length=∫02 1+(7)2dr arc length=∫02 50dr arc…

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: 3. Find the arc length of the curves x = e-2θ (sinθ+cosθ), y=e-2θ(sinθ-cosθ) over the interval 0 ≤ θ…

A: Let       xθ=e-2θsinθ+cosθ  and  yθ=e-2θsinθ-cosθ . Since where L is arc length and a≤θ≤b Now solve…

Q: Find the exact arc length of the curve over the stated interval. 1 1 +y2, from y = 1 to y = 4 x = 4°

A:

Q: 1. Find the arc length of the curve y = on the interval [0, 60]. n i len

A: Answer is 168 Explanation is given below..

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: The area of the rotational surface resulting from rotating the arc of the curve x=cos^3 t, y=sin^3 t…

A:

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