find Ihe revolving Ihr y-axis; of he surface gesnerated bog The cumve y = x% + Y2 aboul- area

Q: Find the area of the surface generated by revolving the given curve about the y-axis. x = 2y + 3, 0…

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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. - 10 10 cos (0),…

A: Find the derivatives with respect to θ

Q: Find the between the two curves. area 2. X=ay, a'y=x 3

A: The area between the curves can be calculated by integration. The formula used for the integration…

Q: Without using a calculator, for the following, find the area of the surface obtained by rotating the…

A: We need to find surface area.

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: The base of a solid is the region in the first quadrant between the graph of y and the raxis for 0<…

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Q: Find the area of the surface generated by revolving the given curve about the X - AXIS. Y 8x, 0 < a…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V6 - x, 4 <…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V6 - x,…

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Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: Q2 Find the area of surface generated by revolving the curve y=√x+1,1< x≤ 5 about x-axis

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² -…

A: The given curve is y2=9x2-a2 in the first quadrant. We need to find the surface area when the given…

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

A: Calculate surface area: S=∫-772πx1+dxdy2dy   =∫-772π49-y21+ddy49-y22dy   =∫-772π49-y21+-y49-y22dy…

Q: Find the point(s) on the surface xyz = 1 closest to the origin.

A: Given, g(x,y,z): xyz=1 distance from origin is  d=x2+y2+z2 f(x,y,z)=x2+y2+z2  square of distance…

Q: Find the area of the surface generated by revolving the given curve about the y-axis. x = 4y +3, 0≤…

A: Let us consider a curve g(y) on the interval [c,d]. The surface area of the surface of revolution…

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y = -…

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Q: Q:Find the that is POT HOh of the curve area of the suoface generated by revolving the Y=x² between…

A: Using area formula we have

Q: A conical funnel is formed by rotating the curve y = 1/3 x about the y-axis. The radius of the rim…

A: We have to given the curve y = 1/3 x about the y-axis. The radius of the rim of the funnel is to 6…

Q: 4x with 0 < x< 3 about the x-axis. 3 Find the area of the surface generated by revolving the curve…

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Q: Find the area of the surface obtained by revolving the curve y=2/4=x, for 1<«<4, around the x-axis.…

A: Explanation of the solution is given below...

Q: Q3) find the soluation of differention equation 1) 2y' = y cot(x)

A: To find the solution of the differential equation 2y'=y cot(x) Formulae used : ∫dxx=ln |x|∫cot(x)=ln…

Q: x = e* + e=t Find the exact length of the curve for – 2 <t < 0 y = – 7 – 2t arc-length =

A: We use the formula of arc-length of a parametric curve to answer the given question

Q: The area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: Area of ellipse initially  = Ai  = πab    Now, lengths of axis are changed,   They are  [ 2(1.0099)a…

Q: y = V8 - x, 2 <x S 8

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Q: i) The area of the surface obtained by the rotating the curve y=V 16-x², -1s×<1 about the x-axis is

A: As per the company's guidelines, we are supposed to solve first question for you,  kindly repost the…

Q: Find the area of the surface obtained by rotating the curve about the y-axis. = (y² - Iny), 1 ≤ y ≤…

A: surface area  about  y axis  bounded by  x=g(y)Area=∫ab 2π g(y)1+g'(y)2  dy

Q: 2. Determine the arc length of the given curves a) y =+ 1<y< 2 3

A: s=∫y1y2 1+x'2 dyy'=3y23-14y2y'=y2-14y2s=∫121+y2-14y22dys=∫121+y4+116y4-2×y×14y dys=∫12y4+116y4+12…

Q: Find the area of the surface generated by revolving the curve about the indicated axis. 8) y = 3x -…

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Q: Find the area of the surface generated by revolving the curve - 5x y = e x > 0

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Q: 2.lexPress the faiauing curve inthe form of Yara meter eQuation al Y=1-×モン-2 b.) y? zzg,x>4

A: Solution given below

Q: Consider the parameterization for the cycloid given as: x = 4(1– sint) y = 4(1-cost) 0<t<2n a) Find…

A: Given curve is x=4t−sint and y=41−cost, 0≤t≤2π (a) We have to find the area of the arch of the…

Q: Find the area of the surface formed by rotating the curve with the equation x ^ (2) - (y ^ (2)) /…

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Q: (d) Find the area of the surface generated by revolving the curve y = 2a, 0 < x < 3, about the…

A: Part (D) To find the area of the surface generated by revolving the curve, y=2x,0≤x≤3, about the…

Q: W Parkmdrc ey da klat 0KV41 Dater mine the area A the sur face 区E 242Y

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Q: Find the area of the surface generated by revolving the given curve about the x-axis. y = V9 -x,…

A: 3

Q: Find the exact arc length of the curve 2xy = y² + 4 over the interval 2 ≤ y ≤ 4. Find the area of…

A: Given: 2xy=y2+4 over 2≤y≤4 to find the arc length of the curve and given the another equation is…

Q: 1. Find the equation of the tangent plane to the surface cosh [exp (x²y)] = Z y? at the point where…

A: We will find out the required equation of tangent plane.

Q: Find the area of the surface obtained by rotating the curve from x = 0 to x = 1 about the x-axis.…

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Q: Find the length and the cuur vature of the Smooth eurve rCt) = (snt)i t(5 cost); + (sint)K from o to…

A: Given curve is rt→=sinti+2costj+sintk and given t from 0 to 2π We have to find the length and…

Q: メ y= oL Xとn2

A: Given curve is y=ex , 0≤x≤ln2find the area of the surface

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0 ≤ x ≤ 1…

A: The formula for the surface area of the rotating object from the curve y=f(x) with the constraint…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0< x <1…

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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. Round your…

A: Consider the provided question, We have to find the surface area obtained by rotating the given…

Q: for the Surface Area below .. what is * ?the radius of revolution Q3/ The arc of the curve x=Vy,…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis 1 = (e…

A: Given y=112e6x+e-6x  ,for -2≤x≤2  Area of surface of curve when revolved about x-axis…

Q: Find the area of the surface generated by revolving the curve x = 9y +1; 0 < Y< 12 about the y-axis.…

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Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + e*, 0 <…

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Q: Find the area of the surface generated by revolving the given curve about the y-axis. x = 8y + 3, 0…

A: Note: If x=fy≥0 and continuously differentiable on a,bThe area of the surface generated by revolving…

Q: Consider the curve y = 3 sin(2x), where 0 < x < T/2. Find the surface area when this curve is…

A: To find the surface area when the curve the is rotated about the x-axis.