Find the length of the parametric x = e*, y = e=t, z = /2t, where 0

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A: Given data: The x-coordinate of the curve is x=cos t+tsin t. The y-coordinate of the curve is y=tcos…

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Q: Evaluate the unoriented line integral (22 + y° + z²) ds (2x² along the parametric curve a : [0, 1]…

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A: using the formula to determine surface area revolving to y axis S=2π∫abx(t)(dxdt2+dydt2)dt

Q: Given the integral representing the length of the parametric curve x = t,y=t", 0 < t <1 A dt [4¢ + 9…

A: Length of parametric curve , L= ∫abdxdt2+dydt2 dt

Q: x(t) cos(t), y(t) = 1+ sin(t), with 0 < t < 2n

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Q: Which of the following integrals represents the length of the parametric curve x = t -t, y= t2, 1<t<…

A: Here we use the formula for find the length:

Q: Find the arc length of the curve on the given interval. Parametric Equations      x = e−t cos t, y =…

A: We have given;

Q: Use a calculator or CAS to evaluate the line integral correct to four decimal places. x sin(y + z)…

A: find the explanation below

Q: Find the area under the parametric curve x=t(1+t) , y=1/(1+t) ,  between t= [0,1]

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Q: Find the coordinates of the centroid of the curve x = e^t cos t, y = e^t sin t, 0&lt;=t&lt;= pai.

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Q: 3) Find the radius of curvature for the parametric X = сurve e-t cos t , y = e=t sin t.

A: R=1+dydx232d2ydx2 Given equations of curve- xt=e-tcostyt=e-tsint

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Q: Compute the arclength of the curve in the plane given by C = {(r, y) = (t² cos(t), t² sin(t)) for 0…

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Q: Give the integral representing the length of the parametric curve x=t^3, y=t^4, 0≤t≤1.

A: Given: A parametric curve:   Now the length of the parametric curve is given by the formula:

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Find the equation of the tangent line to the parametric curve at (1,3). 2=1+ Int y =t² +2

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Q: 3) Find the radius of curvature for the parametric сurve e-t cos t y = e-t sin t.

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. x? from the origin to the (a) Find a vector parametric…

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Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0 … t ……

A: coordinates of the centroid of the curve  x=cost+tsinty=sint-tcost…

Q: Find the arc length of the parametric curve. x = e', y = e, z = v2t; 0<t < 8

A: Here, the given parametric equation is: x=et, y=e-t,z=2t, 0≤t≤8 The formula for the arc-length is…

Q: Set up the definite integral(s) equal to the arc length of the curved defined by the parametric…

A: Use the formula of arc length in parametric form and simplify.

Q: Which of the following integrals represents the length of the parametric curve z = 1+e, y=ť, 3 <t<…

A: In order to know the length of the given parametric curve we will use the formula  where  -----

Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. Find a vector parametric equation for the parabola y = x²…

A: The solution is following.

Q: Find the area enclosed by the given parametric curve and the x-axis. x = 5 sin(t), y = sin(t)…

A: To find the area between the parametric curves

Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

Q: Set up, but DO NOT EVALUATE an integral to compute the arc length of the curve given by the…

A: See below the answer

Q: 3. Find the arc length traced out by the endpoint of the vector-valued function 1 †(t) = t cos t î +…

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Q: Find the line integral with respect to arc length ∫C(6x+4y)ds, where C is the line segment in the…

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Q: Find the center of gravity of the region bounded by the x-axis, the curve y = sec x, and the lines x…

A: Consider the given question,The graph of the curve y = sec(x) and the line x = -pi/4, x = -pi/4 is…

Q: Find the arc length of the parametric curve. L x = 4 cos(t), y = 4 sin(t), z = 3t; 0≤t≤ T

A: Given problem:- Find the arc length of the parametric curve.   x = 4cos(t), y = 4sin(t) , z = 3t ; 0…

Q: | 5y? dx +xy dy

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Q: Find a parametrization for the curve y = Vx with terminal point (0, 0) using the angle 0 in the…

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Q: Find the arc length of the parametric curve. x = cos' t, y = sin° t, z = 2; 0 < t < T/2

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Q: 4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) =…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: ) For parametric curves x = t + \t, y = t – \t,and 0 <t< 1set up an integral hat represents the…

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Q: Evaluate the unoriented line integral +y² + z²) ds along the parametric curve a : [0, 1] → R³ with…

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Q: Suppose F(2, y) = -y sin(æ)i + cos(2)j. (a) Find a vector parametric equation for the parabola y =…

A: Given F→(x,y) = -ysin(x)i→+cos(x)j→ a) Let us assume x=t then y=x2=t2 by differentiating r→(t) with…

Q: Find the tangent line equation to the parametric curve cos t y = sin t at t = O A. y = x+ O B. y =…

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Q: Find the line integral with respect to arc length (2x + 7y)ds, where C is the line segment in the…

A: Given end points of line segment are  P=8,0 and Q=0,3

Q: (2x + y)dx + (x + 2y)dy

A: Given integral is:  where C is any curve that joins the point (1,1) with the (2,2).

Q: Find the arc length of the parametric curve. x = 3 cos(t), y = 3 sin(t), z = 4t; 0<t<+ L =

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Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0…

A: Given,

Q: Find the line integral with respect to arc length (2x + 6y)ds, where C is the line segment in the…

A: The solution of line integral is given as follows :

Q: The area of the surface obtained by rotating the curve y = et +e asxsb, about the x-axis is 1/2 e2 +…

A: Find the surface area rotating the curve about x axis

Q: Find the area under the curve for the parametric function defined by the equations x(t) = t³ +t + 1,…

A: Given parametric function is  x(t)=t3+t+1 and y(t)=t2-t  where t€[1,2]