(a) If a > 0, find the area of the surface generated by rotating the loop of the curve 3ay = x(a – x) about the x-axis. (а—Зх) 2/3ax (b) Find the surface area if the loop is rotated about the y-axis. na“ 3

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: 3. Find the area of the surface generated by revolving about the y-axis the part of the curve y = x?…

A:

Q: The area of the surface obtained by rotating the curve y = 22 x + 1, 0 < x < 44 about the x-axis is

A: Consider the given curve. y=22x+1 in the interval 0≤x≤44 The problem requires to find the area of…

Q: 3. Find the area of the surface generated from revolving the curve y = x ++4 from x = 1 to x = 2…

A:

Q: 11. Find the area of the surface obtained by rotating the curve y = a, 0 < a < 3/4, about the a…

A: Surface area of revolution

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 2 + 2)3/2, 1s ys…

A: The curve x=13y2+232 revolved about x-axis on 1≤y≤4

Q: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 2 + 4y2,…

A: To find the exact area of the surface obtained by rotating the curve about the x-axis. x=2+4y2    ,…

Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y=x3,…

A: If the curve y = f(x), a ≤ x ≤ b is revolved about the x-axis, then the area of the resulting…

Q: 1. Find by integration the area of the surface of revolution generated by revolving the loop about…

A:

Q: 5. Find areas of the surfaces generated by revolving the curves about the indicated axes x =t+V2…

A:

Q: (c) : Find the area of surface generated by revolving the curve about x- xis y = Vx - x3/2, 1< x <…

A: c) Given y=x-13x32, 1≤x≤3 y=f(x) is a continuous function in the interval [a,b] S=2π∫aby1+y'2dx…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x³, 0 < x <…

A:

Q: 2. The surface area of the surface generated by revolving the curve y = x, -1 < x<1, about the…

A:

Q: 6. Find the area of the surface generated by revolving the curve y = x² + 2 from x = 1 to x = 2…

A:

Q: Q4:B/ Find the area of the surface generated by rotating the curve y = e", 0 < x<1, about the…

A:

Q: 3. Find the area of the surface generated by revolving the curve = 2/1- y (-1 < y < 0) X about the…

A:

Q: The area of the surface obtained by rotating the curve y = V25–x2, -4 < x s 4 about the x-axis is

A:

Q: 1 Find the area of the surface obtained by rotating the curve y = 6. 1 <x < 1. about the x-axis 2x

A:

Q: Find the surface arca of y = (1/3)r 10<x <1 revolved about the z-ax

A: Given: The equation is y = 13x3 , 0 ≤x≤1 revolved about the x - axis.

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

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3,    0 ≤…

A:

Q: 3. Find the area of the surface generated from revolving the curve y =x++ 4 from x 1 to x 2 about…

A: Given, Curve ,y=x33+14x+4 To find : Area of surface generated after revolving the given curve from…

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

A:

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: The area of the surface obtained by rotating the curve y = v64-x2, -2 <x < 2 about the x-axis is

A:

Q: 1. Find the surface area of the solid obtained by revolving the curve y = √25-x from = 9 to x = 16…

A:

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

A:

Q: 5. Find the exact area of the surface obtained by rotating the curve y = V16 x2, -2<*<2 about the…

A:

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

A:

Q: 6. Find the exact area of the surface obtained by rotating the curve, y = x³, 0 < x < 2, about the…

A:

Q: The area of the surface obtained by rotating the curve y = V4-x², -2 s xs 2 about the x-axis is

A:

Q: Find the area of the surface generated by rotating the portion of the curve y = (x^3)/3 from x = 0…

A: Consider the given curve y=x33 , x=0 to x=1 First, find the first derivative of the curve with…

Q: 8) Find the area of the surface generated by rotating about the x-axis the arc of the curve y x…

A:

Q: Find the area of the surface generated by revolving the curve y=- 24 .Osxs/6. about the x-axis.

A: area = ∫06 ydx area = ∫06  x3dx/24 area = [x4/96]60 area = 6*6/96 - 0 area = 3/8

Q: Sketch the curve y2 = x(x-4)2 and find the volume of the solid of revolution formed when the closed…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = cos -х 0< x…

A:

Q: Find the area of the surface obtained by rotating the curve y =÷x/2 – x³/2 for 0 < x < around the…

A: We find dy/dx using power rule

Q: 13. Find the area of the surface generated when the curve = , on [2,4] is rotated about the y-axis.

A: The solution are next step is

Q: 3. Find the surface area of the surface generated by revolving the graph of the "curve" given…

A: The given parametric curve is: x=t,     y=t2,         0, 2

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 area of the surface generated when the curve y=1/4(e2x + e−2x)is rotated about the x-axis…

A:

Q: Find the area of the surface resulting from rotating the curve: x=5t−1, y=2t^3, -2≤t≤1, around the…

A:

Q: ii) Find the exact area of the surface obtained by rotating the curve 1 12x 3 y = x³ + 9 1 ≤ x ≤ 2,

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Q: The exact area of the surface obtained by rotating the following curve 6x = y + 12, 2 < x < 3 about…

A:

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

A:

Q: ii) Find the exact area of the surface obtained by rotating the curve y = x³ + 1 ≤ x ≤ 2, 1 3 12x 9

A: Use Area of surface  formula.

Q: Find the area of the surface obtained by rotating the curve y² = 4x + 4 0<x<8 about the x-axis?

A: