Q:3: a) Find the surface area of the object obtained by rotating x=e2y, -1sys 1 about the y-axis.

Q: 4- The centroid of the shaded area is required to lie on the y-axis. Determine the distance b that…

A: Answer is mentioned below

Q: given ∫∫s (x2z) dS and S is the part in z = sqrt(x2+y2), which lies in x2+y2 = 1 calculate the…

A: we have to evaluate ∬Sx2zdS Now, we have z=x2+y2 ⇒z2=x2+y2∂z∂x=xz and…

Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

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Q: Find the surface area of the portion of the paraboloid given by the equation z = 1– x2 – y² that is…

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Q: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y = 2r² (0 <t s…

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

Q: Find the area of the surface generated by revolving x = t+2/3, y = +2/3t+3, -2/3 sts2/3 about the…

A: The surface area of disk is s=πr2 h  where r is radius and h is width

Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

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Q: Find the area of surface that is generated by revolving the portion of the curve 9 – y² , – 2 < y< 2…

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Q: Find the area of the surface generated by revolving x =t+ 2/5, y= +2/5t, -2/5 sts2/5 about the…

A: Here we will find out area of surface of revolution.

Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

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Q: Determine the area of the surface with parametric equat ions x = 2u?, y = v², z = 2uv, %D 0<u< 3, 0<…

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Q: Determine the surface area generated by revolving the line segments about y-axis. 3m 4m 2m 1m 2m 2m…

A: Given , Line segment revolve around y-axis , we have to find surface area of formed shape .

Q: Find the area of the surface generated by revolving the curve y = cos(r), 0<aS5 about the r- axis.

A: The solution is given below in the next step:

Q: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: Q4(a) Find the area of the surface generated by revolving the curve, x = /6y – y2 ; 2<y<5

A: Given the curvex=6y-y2    , 2≤y≤5we need to find the area by revolving the curve about y axis from…

Q: Find the area of the surface generated by revolving the curve, x = /6y – y? ; 2sys 5

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the…

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Q: Find the area of the surface generated by revolving the curve                             x = 4t, y…

A: If x = f(t), y = g(t) then surface area is 1) About x axis: A=2π∫abydxdt2+dydt2dt 2) About y axis:…

Q: If the curve y = f(x), a ≤ x ≤ b, is rotated about the horizontal line y = c, where f(x) ≤ c, find a…

A: Given, Curve y= f(x) , a≤x≤b Rotated about a horizontal line y=cwheref(x)≤c

Q: Find the area of the surface generated by revolving the curve about each given axis. x St, y 2t, 0st…

A: Given that        x = 5t , y = 2t  , 0 &lt;= t &lt;= 5  Here we have to find the area of the surface…

Q: Find the surface area of the object obtained by rotating y = +÷, 1 1<x<2 about the x-axis.

A: To find the surface area of the object obtained by rotating y=x36+12x ,  1≤x≤2 about x-axis.  Let,…

Q: Find the area of the surface obtained by rotating the curve y 4V7,0 < I < 5, along the r-axis.

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Q: Find the isogonal trojecdories of x*+y² =r² at 45",

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

A: Use formula of surface area revolved about x axis

Q: HW: Find the area of the surface generaled by revolving 3DVy, 1 <y<8 about the X- axis. 1. 3.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Which one, y=ex, 1≤y≤2, gives the surface area of the solid formed by rotating the curve segment…

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Q: 35. Find the area of the surface generated by revolving the para- metric curve x =t, y = 21² (0 <…

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Q: Find the surface area of the cone frustum generated by revolving the line segment y-/2) + (1/2, 1…

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Q: Find the area of the surface generated by revolving x = t+2/3, y =+2/3t+1, -2/3 sts2/3 about the…

A: Find the area of the surface generated by revolving the graph of the following parametric equation…

Q: V9, 0< y< 4 Find the area of the surface generated by revolving the curve x = about the у-ахis.

A: We have to find the surface area.

Q: Find the area of the surface generated by revolving the parabolic arc y = x 2 for 0≤x≤ 1 about the…

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Q: Find the surface area of the portion of the cone 22 = 4x² + 4y? nat is above the region in the first…

A: Given: The portion of the cone is Z2=4x2+4y2 which is bounded by the line y=x and the parabola y=x2

Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: Find the area of the region enclosed by the parametric equation x = t3 – 8t y = 6t2

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Q: Find the surface area generated by rotating the semi-circle x = (49 – y² be- tween -7 < y < 7 about…

A: To Determine :-  The surface area generated by rotating the semi-circle x = 49 - y2 between -7 ≤y ≤7…

Q: Compute the surface area of the surface generated by revolving one arch of the cycloid…

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Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: 35. Find the area of the surface generated by revolving the para- metric curve x = t, y = 21² (0 < 1…

A: Given: x=t y=2t20≤t≤1

Q: Find the area of the surface of revolution generated by revolving C = {(x,y):x = y = 1- 2t, -1sts1}…

A: Given that C=x,y:x=-3+4t3, y=1-2t, -1≤t≤1 about the line x=2. The range of y is,…

Q: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y= 21² (0 <…

A: Given: The curves,  x =t,  y = 2t2,   0 ≤ t ≤ 1 To find: The area of the surface generated by…

Q: Find the surface area of the object obtained by rotating x = Vy-6 2sys3 about the y-axis.

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Q: find the surface area obtained by rotating the circle (x – 4)2 + y? =1 about the y-axis. %3D

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Q: "ind the area of the surface generated by revolving the curve x = 2/1- y, –1< y <0 bout the y-axis.

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Q: • Find the area of the surface generated by revolving about the x-axis the upper half of the ellipse…

A: IN THIS QUESTION WE HAVE TO FIND AREA FROM REVOLUTION OF A ELLIPSE.

Q: Q#4 a. Find the area of the surface generated by revolving abuut the x – uxis the portion of the…

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

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