dr. Let f(z) =z. Find from z-0 to Z-4+2í alongthe curve C given Z=21 to z=2i

Q: Find fe F dr for F = 7yi - (sin y)j on the curve counterclockwise around the unit circle C starting…

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Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: et C be a portion of a curve from (2,0) to (2,2). Let F(r, y) = (tan(2?) +2, ) Is F conservative?…

A: In the given question, the concept of integration is applied. Integration Integration is a method of…

Q: find the arc length of the curve on the given interval y = (x2+2)3/2/3 on [0,1]

A: Given curve is: y=(x2+2)323 from x=0 to x=1Heredydx=32(x2+2)12×2x3=xx2+2

Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

Q: Find the length of the curve over the given interval. r = 4 sin θ, [0, π]

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Q: Find the length of the curve. x = cos t y = sin t

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Q: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.

Q: Use the guidelines of this section to sketch the curve. y = e-X sin(x), 0 < x < 2 y y 1.0 1.5 0.5…

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Q: 4) Consider the curve given by: cos(xy) = x(y – 7) – 1 %3D Find y' dx a)

A: Given function is cosxy=xy-π-1 Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: Find the length of the curve x = cos t, y= sin t, 0 <IST. 4/2 4 IT 2/2 IT 2 2

A: Given that: x=cos2t, y=sin2t, 0≤t≤π

Q: 10. Find the length of the curve defined by x = Vt, y = 1 – t from t = 0 to t = 5. %3D

A: To find: The length of the below curve from t = 0 to t = 5.

Q: a) Show that the length of the arc of the curve y=f(x) where S(x) = Insecx 0SxS is 4 In(1+ v2)

A: We need to show that the length of the arc of the curve y=f(x) where f(x)=ln(sec(x)), 0≤x≤π4. The…

Q: Use Green's Theorem to evaluate F. · dr, where F = (Va + 4y, 2x + and C consists of the arc of the…

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Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

Q: Find Sc F · dr for F = 3yi – (sin y)j on the curve counterclockwise around the unit circle C…

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Q: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: The Tschirnhausen cubic is the curve given by the equation x^2=y^3+3y^2 At which point(s)…

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Q: Find T,N and k for the curve: 1- r(t) = (6 sin 2t)i + (6 cos2t) j+5tk.

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t

A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…

Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

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

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Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: Find the point on the cycloid c(t) = (t − sin t, 1 − cos t) where the tangent line has slope 1/2.

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Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

Q: Consider the curve where a =0 (a) Compute(t) at t = [0, +∞). (b) Find the tangent line at the point…

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Q: Calculate the length of the curve r=a*sin(^3)(x/3) for (x(1)=0, x(2)=3pi)

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Q: Prove that all normal to the curve x =acid+at sin t, Y=a sin t-atcost.Are at a distance a from the…

A: We need to prove that normal to the given curve are at a distance of a from origin.

Q: * Find the length of the curve.7 (ähäs 3) f(x) = In(sec x) %3D 4 In(3 + 1) O In(3 + 2) O In(2 + 2) O…

A: Hence option (d) is correct.

Q: Sketch the curve. O 68°F r = 2 - 2 sin(0) -2 -3 1 y 1 2 1 1 XX 2 O EZ 1 2 3 3 X -2

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Q: Find T, N and B for the curve F(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t -0 Give your answers…

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Q: Let C denote the curve of intersection between x = -5z° and y = 6z", starting from A(0,0,0) and…

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Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…

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Q: Find the length of the curve x = 8 cos t + 8t sint,y= 8 sin t – 8t cos t ; 0 < t %3D -

A: The length of the parametric curve is given by  L=∫abx't2+y't2dt.

Q: Determines the length of the curve in the indicated interval x = 3 sin t+ 3t, y = 3cos t, 0stsm O 12…

A: Given curve is x=3sint+3t and y=3cost, 0≤t≤π. We have to determine the length of the curve on the…

Q: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

A: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.

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Q: 7. Find the length of the curve f(1) = In(sin r), 0 < r < a/6.

A: Topic = Application of integration

Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: 2. Let y be the curve in R3 given by t (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds

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Q: he length of the curve y = sin(3X) from x = 0 to I= is given by

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Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

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Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: A curve in space is given by C = { (r, y, z) = cos(nt) ', In(10 – t²), ² + 4 for t € (0, v10) Give…

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Q: et +e- find the length of the curve h(x) = from r = 0 to z = In 2.

A: The standard formula for arclength will be used in solving this problem. The typeset solution is…

Q: 3) Find the arclength of the following curve on the given interval. x = 31, y= 41; 1<t<4 X =

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Q: what is the length of the curve y=1-cos(x) from x=0 to x=4pi

A: Given: y=1-cosx To find: We have to find the length of the given curve from x=0 to x=4π.