5. Find areas of the surfaces generated by revolving the curves about the indicated axes x =t+V2 :-/2 stsV2 about the y- axis +V2t a)

Q: Find the area of the surface generated by revolving the curve y = /2x – x2, from x = 0.25 to x =1.7

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

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Q: 10. у %3D /5 — х, 3 <x < 5

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Q: Sketch the recion enclosed by the given curves. Decide whether to integrate with respect to rwr.Daw…

A: Draw all the regions first then decide which region satisfy all the curves

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 the area of the surface obtained by rotating the curve }=2,3 from z = 0 to z = 1 about the…

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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: Find the area of the portion of the cylindrical surface y = 4 - x2 in the first octant that is…

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Q: Compute the length of the circle of radius r defined parametrically by = 3 cost, y = 3 sint ; 0 s t…

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Q: Find the points on the surface ry + yz + zx – x - 22 = 0 where the tangent plane is parallel to…

A: Given surface is  Fx, y, z=xy+yz+zx-x-z2 and we have to find the points on this surface where the…

Q: A point moves along the intersection of the elliptic paraboloid z = 3x² + 5y² and the plane y = 4.…

A: We are given the curve Z=3x2+5y2 and y=4   Now we know that the rate of change is simply derivative…

Q: 6- Find the avea of the Surface of revolution genetaled by revalving the x-axis the arc abaut from…

A: To find - Find the area of the surface of revolution generated by revolving about the x-axis the arc…

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x² between…

A: Solution: Consider the given curve y = x2 The curve revolving between x = 1 and x = 2 about the…

Q: 5- Find the area of the surface generated by revolving the curve X= (y*/4) +1/ (8y²),1<y <2 ,about…

A: Given:function: x=y44+18y2Interval: 1≤y≤2To find : Area of surface generated by revolving the curve…

Q: Find the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: A thin plate part with a mass density equal to 1 and shape as shown in Figure 2 has an edge curve C…

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Q: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

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Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: 3. Find the length of the curve y = x – In x, 1<x < 4. 1. Find the area of the surface obtained by…

A: The solution is given as follows

Q: Let S be the surface obtained by revolving the plane curve 2x = /9 – y² about the y-axis.

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Q: Which type of surface does the curvex= cos(3t),y= sin(3t),z=t, lie on?

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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: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

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Q: Find the area of the surface generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

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Q: A point moves along the intersection of the elliptic paraboloid z = 10x? + 3y² and the plane y = 1.…

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Q: 4. Find the area of the surface generated by revolving the curve y = v9 – x², - 2 < x < 2, about the…

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Q: Find an equation of the tangent plane to the given surface za² + y² +1 at (1,1,3).

A: Given equation of the surface is  z=x2+y2+1 We have to find the tangent plane of the given surface…

Q: Suppose div F = 0 in a region enclosed by two concentricspheres. What is the relationship between…

A: Apply the divergence theorem for the hollow region which is bounded by 2 surfaces. Consider D as the…

Q: y = N|XW --- - 6x 1 <x<1

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Q: 5. Find the area of the surface of revolution generated by revolving .3 y = on interval [0,3] about…

A: Given: The function y=x33on interval 0,3, To find: The area of the surface of revolution generated…

Q: 4. Find the area of surface that is generated by revolving the portion of the curve I = 2/1- y,…

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Q: 7. Find the surface area of the cone frustum generated by revolving the line segment x 1 y ==+ 1s…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 4t, y = 7t,…

A: x=4t y=7t

Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

Q: Find the areas of the surfaces generated by revolving the curves about the indicated axesx = t + √2,…

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Q: 6. Find the area of the surface formed by revolving about the curve defined by y = x2 - x2, 1<x<3…

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Q: Let C be a curve given by the intersection of the surfaces z = x2 +y2;z = 3−2x . The value of the…

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Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

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: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

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Q: x = 1+ 2y2, 1< x < 2 about the x-axis.

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Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

Q: find the areas of the surfaces generated by revolvingthe curves about the given axes. x = √y, 2 ≤ y…

A: We first find dx/dy

Q: Give arc-lengtu porametriz atian of the line which an Hhe tangent planes of and (1,2,9). is Hhe…

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Q: Find the surface of revolution of the curve y = 4 + 3x² that is rotated about the y- axis between 1…

A: We have to find the area of the surface of revolution of the curve y=4+3x2 that is rotated about the…

Q: Determine the area bounded by the conic sections y = x² – 6² and y = 6² – 2². O 576 O 183 O 281 O…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 6t, y = 9t,…

A: Here,  we need to find the surface generated by revolving the curve x=6t, y=9t, 0≤t≤3, about each…

Q: 2. Find the area of the surface obtained by rotating the curve: y = Vx +1,1<x<5 about the Х-ахis

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