The curve y = V4-x², -1

Q: Find the arc length of the graph by partitioning the x-axis.   9y2 = 4(1+x2)3 , from x=0 to x=4√2…

A: Given: 9y2=4(1+x2)3  from x=0 to x=4sqrt(2)

Q: Find the arc length of y³ + y = x² + 6x on the interval [-5, –1].

A: Since the given graph is in implicit form (we can not find the explicit value of y in terms of…

Q: The area of the surface obtained by rotating the curve y = 1sxse about the line x = 42 is

A: Given that y= 1/x  + x3 /12 and find the surface area. Here i attached solution of this question.

Q: Find the area of the surface of revolution generated by revolving the curve y = 5/ 0Sa<4, about the…

A: Given that:  y=5x,                        0≤x≤4

Q: Find the exact value of the surface area generated by revolving the given curve, about the x-axis. 1…

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Q: Find the area of the surface generated when the given curve is revolved about the y-axis 1 y=(8x)…

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Q: y = V4-x, -l&xs1 about the x-axis

A: We'll answer the first question since the exact one was specified. Please submit a new question…

Q: The area of the surface obtained by rotating the curve y = x2, 0sxs1 about the y-axis is

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Q: Find the arc length of y3 + y = x2 + 6x on the interval [ -5, -1 ]. Also, determine the surface of…

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Q: Find the arc length of the curve y 1 on the interval [1, 2]. %3D 4x2

A: Given:    y = x4/8 + 1/4x2   Interval : [ 1 , 2 ]

Q: Find the arc length of the curve x = -2y³/2 from y = 0 to y = 10. Length =

A: The given curve is x=-2y32 from y=0 to y=10. Find the arc length. As we know the formula of arc…

Q: Find the surface area generated when the arc given by y = 2/15 – x; 0 <x < 15, is revolved about the…

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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 arc length of the graph by partitioning the y-axis. (x+9)2=4y3 , from y=0 to y=1 ; x  ≥ −9

A: GIVEN THAT (x+9)2=4y3  WE HAVE TO FIND ARC LENGTH

Q: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

Q: Find the area of the surface generated by revolving the curve y /2x-x, 0.25 sxs1.5, about the…

A: Use surface area formula about x asis

Q: Find the area of the surface generated by revolving the given curve about the x- axis: y = 19 – x²,…

A: Given,y=9-x2   squaring both the sides,y2=9-x2x2+y2=9x2+y2=32this is the equation of the circle with…

Q: Find the area of the surface generated by revolving the curve about each given axis. x= 5t, y- 9t,…

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Q: Find the arc length of the curve y=sqrt (4-x^2), from 0≤x≤2.

A: Solve

Q: Determine the surface area generated by revolving the arc 3y= 4x from x=0 to x=3 about the x-axis.

A: To find- Determine the surface area generated by revolving the arc 3y = 4x from x=0 to x=3 about the…

Q: Find the area of the surface formed by revolving the graph y=x on the interval [0,3] about 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…

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

Q: The area of the surface obtained by rotating the curve y = 25-x² , -4 sx<4 about the x-axis is

A: Area of the surface rotated about x -axis is, a≤x≤b,…

Q: Find

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Q: Find the arc length of y³ + y = x² + 6x on the interval [-5,–1].

A: The arc length, L of a function, x=f(y) in the interval [a,b] is calculated using the formula below.…

Q: The curve y V4 – x², – 1 < x < 1, is an arc of the circle x² + y? = 4Find the area of the = 1…

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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: Solve the area of the surface of the revolution generated by revolving the arc of the curve, x= y³…

A: A detailed solution is given below.

Q: Find the area of the surface generated by revolving the curve - 5x y = e-b", x > 0 around the -axis.

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Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: Find the surface area of the cone frustum generated by revolving the line segment y = 4 1 over 1 < x…

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Q: Find the area of the surface generated by revolving the curve y=x3/3 from x=0 to x=1 about the…

A: To find the area of surface generated by y=x33 and x=0,x=1 about x-axis A=∫012π·y·dS, dS=1+y'2·dx,…

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: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: Find the area of the surface generated by revolving the curve y = /8x – x² on the interval sa <…

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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: Find the area of the surface formed by revolving the graph of y = Vx + 2 on the interval [1,8] about…

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Q: Find the length of the circle of radius r defined parametrically by x=rcost, y=rsint,0≤t≤2π.

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

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: 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: 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: Calculate the circumference of a three-quarter circle with the radius r = 3 using a curve integral…

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

A: y2=12x ⇒y=23x ⇒dydx=3x ⇒dydx2=3x2 ⇒dydx2=3x ⇒1+dydx2=1+3x ⇒1+dydx2=1+3x

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 the exact area of the surface obtained by rotating the curve about the xx-axis.  y=sin(πx/8),…

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Q: Find the radius R, of curvature to the hyperbola y = x + 3x² – x³ at the point x = 0 given that R =…

A: To find the radius R, of curvature to the given hyperbola at point x = 0.

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

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Q: Find the arc length of y^3+y=x^2+6x on the interval [-5,-1]. Using the same arc, determine the…

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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…