Calculate the surface area of ​​the rotating body obtained by rotating the curve given by the parametric equation about the y-axis

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

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Q: Find the area of the surface generated by revolving the parametric curve x = t, y = 2t² (0 ≤ t ≤ 1)…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: Express the curvature of a twice-differentiable curve r = ƒ(u) in the polar coordinate plane in…

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Q: 25) Show that the curve with parametric equations x = tcos(t) , y = tsin(t), lz = t ies on the cone…

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Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x, 0 <xs;…

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Q: Give a parametric description for a cone with radius a and heighth, including the intervals for the…

A: We can parameterise the same as following: Assume s &amp; t as two parameters radius = a and height…

Q: find the areas of surfaces generated by revolving the curves about the given axes

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Q: Find an equation for the tangent plane and find the parametric equations for the normal line to the…

A: I am attaching image so that you understand each and every step.

Q: Show that the curve with parametric equations x = tcost, y = tsent, z = t is z cone z2 = x2 + y2 and…

A: We have to show that the curve with the given parametric equations is a cone with the equation…

Q: Find parametric equations for the surface generated by revolving the curve y = 1/x about the x-axis.

A: When y = f(x) is rotated about x axis, we get a surface with parametric representation is,…

Q: Find the exact area of the surface generated by revolving the curve over the given interval about…

A: Given data: The given expression for the curve is y=(2x-x2)1/2. The given limits of x are [a,…

Q: Find the area of the surface generated by revolving the curve about the y-axis. y=4-x², 0≤x≤2.

A: In this question we have to find the area of the surface generated by revolving the curve about the…

Q: Find parametric equations for the tangent line at (1, 3, 3) to the curve of intersection of the…

A: First, find the function of the surface in three variables, f(x,y,z).  f(x,y,z)=x2y-z Find the…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 y = + /- 2x

A: Given: The equation of the curve y=x36+12x,where  12≤x≤1. Calculation: Compute the surface area as…

Q: Sketch and identify the curve defined by the parametric equations x = sin²t, y = 2 cost

A: Given the parametric equations  x=sin2t y=2 cost To find : Sketch and identify the curve using given…

Q: Find the area of the surface obtained by rotating the curve y = cos(2x), 0≤ x ≤ π/6, about the…

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Q: Find the surface area of the solid that is obtained by rotating the graph of the parametric curve…

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Q: Determine the area of the surface generated by rotating around the "y" axis, the curve described by:

A: Here, the given parametric curve is: x=t33, y=t+1; 1≤t≤2⇒x'(t)=t2, y'(1)=1 Now, the surface area…

Q: Find the area of the surface of revolution generated by revolving the curve r = 2acos(theta) about…

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Q: please find the normal plane equation and parametric equations for the tangent line to the curve…

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Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Find a parametric representation for the surface.

A: To find a parametric equation we have to convert cartesian coordinate to spherical coordinate…

Q: Find the area of the surface generated by revolving the curve

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Q: Find the surface area of the parametric surface †(u, v) = (u + sin(v), v+ sin(u), u – v) where…

A: According to the given information, it is required to find the surface area of parametric surface.

Q: Sketch the parametric curve at R* whose parameterization is given by a (t) = (cos (t), sin (1), t),…

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Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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Q: x = 3 + 2t y = 9– 3t 1<t<4 about y-axis

A: We have to find the surface area of parametric curve.

Q: Let y : IR → R be the parametric curve Y(t) = (, t, t). Find the coordinates of a point P on this…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = + 2 бх

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Q: x =9+2t² y = 4t 0St<2 about x-axis

A: SURFACE AREA OF PARAMETRIC CURVE:                    Consider the parametric curve given by…

Q: Find the curved surface area of the solid generated by revolving the part of the curve y=x² from…

A: Given curve is                                               y=x2 from     (0, 0) to (6, 6) Rotation…

Q: Give a parametric description for a sphere with radius a, includingthe intervals for the parameters.

A: We will use the spherical coordinates for parametrization. Where ρ= radius= a And,

Q: iminate the parameter in x = -t +2t and y =t-4 and then identify the parametric sketch its image in…

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Q: Find the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 8t, y - 6t…

A: Given that, x = 8t y = 6t + 1 0≤t≤1 We have to find the area of surface generated by revolving the…

Q: The area of the rotational surface resulting from rotating x² + y2 = a² about the x axis is? the arc…

A: Given : x2 + y2 = a2

Q: ston Compute the length of the circle of radius r defined parametrically by x = 3 cost, y = 3 sint ;…

A: given that x=3 cost , y=3 sint; 0≤t≤2π find out the length of the circle of radius r i.e. arc length…

Q: 3) Find the radius of curvature for the parametric curve et cost, y = et sin t.

A: To find the radius of curvature. The radius of curvature is the inverse of curvature.

Q: 2. Use parametric equations to derive the formula for the lateral surface area of a right circular…

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Q: Calculate the area of the surface of rotation created by rotating the curved segment about the…

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Q: Find the area of the surface generated by revolving the curve y = 2√x, 1≤x≤2, about the x-axis.

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Q: Eliminate the parameter to find the Cartesian equation for the given parametric curve. = vt +1, y =…

A: Cartesian equations is x^2 - y^2 = 2

Q: What is the solid body surface area formed by rotating the given parametric curve around the y-axis?

A: Given x=costy=sint+t0≤t≤π2

Q: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.

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Q: Find the surface area of the surface generated by revolving a portion of the curve y = x", from x =…

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Q: Consider the curve parametrized by: x = sin t, y = sin2t a. Eliminate the parameter b. Sketch the…

A: x = Sin t  ,  y= Sin2 t(a) Pw  sint = x          y  = x2

Q: Find the exact area of the surface generated by revolving the curve about the stated axis. y = Vx…

A: The formula for area of surface generated by the revolution of curve y=f(x) , a≤x≤b about x-axis.…

Q: Find parametrization of the horizontal circle of radius 4 with center (5, -2, 6). r(t) = %3D

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