Find the surface area of the solid generated the parametric curve: x = e'cost, y = eʻsint, 0

Q: Find the area of the surface obtained by rotating the curve of parametric equations: x = 6t -…

A: Area of surface obtained by rotating the curve is given by

Q: Find the areas of the surfaces generated by revolving the curves in Exercises 31–32 about the…

A: 31.The functions are,

Q: Find the area of the surface obtained by rotating the curve of parametric equations x = 10 cos³ 10…

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Q: Find the area of the surface obtained by rotating the curve from x = = 0 to x 5 about the y-axis. =…

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Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x, 0 <xs;…

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Q: 10. у %3D /5 — х, 3 <x < 5

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

A: We need to find Surface area.

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

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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 surface area of the solid that is obtained by rotating the graph of the parametric curve…

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Q: Find the area of the surface generated by revolving the given curve about the y- axis. x = /25 - y²,…

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Q: Calculate the surface area obtained by rotating the following parametric curve about the y-axis: x…

A: The surface area obtained by rotating the parametric curve x(t) and y(t) about the y-axis over [a,b]…

Q: 3. Find the area of the region bounded by the parametric curve and the y-axis. x=t -4, y = 3t- 4

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the surface area of the solid obtained when the parametric curve x = −2cost; y=2sint for 0 ≤ t…

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

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Q: Find the exact area of the surface obtained by rotating the curve x = (1/3)y^3, 0 &lt;= y &lt;= 1,…

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Q: (2u cos v, 3u sin v, u²) and find tangent plane at Describe/Sketch the surface given by r = (0,6,4)

A: Given, To find: equation of tangent plane ate (0,6,4)

Q: Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for the…

A: We have to find the equation of tangent plane to parametric surface.

Q: valuate the surface integral ! G(x.y.z) do using a parametric

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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 the area of the surface generated by revolving the curve y = 2√x, 1 ≤ x ≤ 2, about the x-axis.…

A:

Q: The area of the surface obtained by rotating the curve y = V16 – x² -1 <x< 1, about the x- axis is

A: The given function is y=16-x2 , -1≤x≤1 rotating the curve about x-axis.

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

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Q: Calculate the surface area of ​​the rotating body obtained by rotating the curve given by the…

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Q: Find the area of the surface generated by revolving the curve about the indicated axis. * = 5, 0sas…

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Q: x =9+2t² y = 4t 0St<2 about x-axis

A: SURFACE AREA OF PARAMETRIC CURVE:                    Consider the parametric curve given by…

Q: Find the area of the surface generated by revolving the given curve about the y- axis. x=2₁√√6-y,…

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Q: Find the area enclosed between the parametric curves x=2t^2 + 6 y=e^-5t and x-axis for t greater…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 8t, y = 7t,…

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Q: The area of the surface obtained by rotating the curve y = 17 x +1, 0SXS 34 about the x-axis is

A: The solution are next step...

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

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Q: Find the area of the surface obtained by rotating the curve x = Va – y², 0 < y s about the y-аxis

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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: Provide a parameterization for the surface formed by revolving the curve y=VX around the X-axis, for…

A: To Determine :-  Provide a parameterization for the surface formed by revolving the curve y = x…

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

A: Given curve is  y=x36+12x Differentiate with respect to x. dydx=x22-12x2

Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: What is the solid body surface area formed by rotating the given parametric curve around the y-axis?

A: Given x=costy=sint+t0≤t≤π2

Q: Find the Surface Area rotating around the y-axis

A: Given curve is

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

A: Solution

Q: x=y"2 -y², 1<y<3 about the y-axis 3°

A:

Q: Find the surface area of the surface generated by revolving a portion of the curve y = x", from x =…

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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 x axis.  y=sinpiex…

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Q: ltermine the surface arca of the solid obtained by rotating y= 19- XZ about the X- axis.

A: Given:- y = √(9-x^2).  To find:- Surface area of solid obtained by rotating about the x axis [-2, 2]…

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: Calculate the area of the surface of revolution obtained by revolving the curve x = 1/3 (y2 + 2)3/2…

A: To find the area of the surface of revolution

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

A: Given that y=x and 0&lt;=x&lt;=3 find the surface area generated by the revolving the given curve…

Q: Find the area of the surface generated by revolving the curve y = 3/x, 1 < x <4 about the x axis.

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.