a) Find the surface area of the object obtained by rotating x = e2y , –1

Q: 4: Show yor work. a) 1: Find the exact area of the surface obtained by rotating the curve y? +x =5,…

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

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

A:

Q: 28. F(x, y, z) = x³i+y°j+z°k, and S is the sphere of radius 3 and centered at the origin.

A: divF→=ddxx3+ddyy3+ddzz3        =3x2+3y2+3z2        =3x2+y2+z2  by divergence theorem,…

Q: Find the area of the surface S where S is the cap cut from the paraboloid z = 2– x – y by the cone z…

A: Given that : z=2-x2-y2z=x2+y2 Now, to find the point of intersection , 2-x2-y2=x2+y2Put…

Q: Find the surface area generated by rotating y=sin x. 0 ≤ x≤ π about the x-aixs.

A: Area of surface problem....

Q: Find the surface area of the solid generated by revolving the cycloid x= a(0- sin g). y =a(1-cos ).…

A: We have to find the surface area of the solid generated by revolving the following cycloid about the…

Q: Find the surface area of the solid that is obtained by rotating the graph of y = f (x) about the…

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Q: HW: Find the area of the surface generaled by revolving 1. Vy, 1 <y <8 about the x- axis. =DX

A: Find the attachment

Q: Consider the solid region E inside the sphere x² + y² + z² = 4 and outside the cylinder x² + y² = 1.…

A: This question is based on 3-D geometry.

Q: 12. Find the surface area for the surface of revolution formed by revolving the curve y = v4 – x?…

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Q: ind the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above the…

A: Using the double integral formula.

Q: Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 x} | about the x-axis.

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Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

A: In the question we have to find the value of area enclosed by the function of given figures.

Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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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: 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 surface area of the solid that is obtained by rotating the graph of y = f(x) about the…

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Q: Find the surface area of the solid generated by rotating the curve y = x² about the y-axis over the…

A:

Q: Under what conditions can you find the area of the surface generatedby revolving a curve x = ƒ(t), y…

A: Given information,x=fty=gt; a≤t≤b To get the area of the surface generated by the curve about…

Q: 2. Use polar coordinates to find the volume of the solid under the paraboloid z = x² + y² and above…

A: Let's find volume of solid by using polar coordinates.

Q: Find the surface area of the part of the circular paraboloid z = x + y that lies inside the cylinder…

A: Solve the given

Q: Find the surface area of the paraboloid z =1-x² - y? that is above the xy-plane.

A:

Q: find the exact area of the surface obtained by rotating x=t^3,y=t^2, 0&lt;t&lt;1 about the x-axis.

A: y=t^2 so t= sqrt(y)x=t^3= (sqrt(y))^3 = y^(3/2)x=y^(3/2) (graphed this equation)

Q: Find the surface area of the surface generated by rotating y = cos x, 0 ≤ x ≤ π/2, about the x-axis.

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Q: The figure shows the surface created when the cylinder y2+z2 = I intersectsthe cylinder x2+z2=1 Find…

A: Given : surface S (say) is created when the cylinder y2+z2=1 intersects the cylinder x2+z2=1 To find…

Q: In exercises 13-18, compute the surface area of the surface obtained by revolving the given curve…

A: Solving part (b) as requested. Given:

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

A:

Q: calculate the surface area of the solid obtained by rotating the curve over the g.iven interval…

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Q: 10. Find the area of the paraboloid x² + y + z² = 2 by the plane y = 0. (Hint: Implicit Surface)

A:

Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a =…

A: Given data: *The graph is f(x)=y=asin(bx2). *The value of the constant a and b is a=8 and b=4. *The…

Q: Find the surface area generated b rotating the portion of the parabolic arc x = y^2 from x = 0 and x…

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Q: The surface area of the solid of revolution generated by rotating 3 x = (y² + 2)ž,1 sys2 about the…

A: Given function is x=13y2+332 where 1≤y≤2. The surface area of revolution of the function is given by…

Q: 2. Find the area of the surface generated by revolving the given curve about the y -axis. (a)…

A: Given b x=y3, 0≤y≤2c x=9-y2, -2≤y≤2

Q: 1. Find the surface area of the cone z = Jx2 + y2 that lies between the plane y = x and the cylinder…

A: Surface area in xy-plane

Q: The surface area of the solid of revolution generated by rotating x = (y² + 2)²,1 < y s 2 about the…

A:

Q: Use polar coordinates to find the volume of the solid under the paraboloid z = x2 + y2 + 1 and above…

A:

Q: Find the area of the surface generated by revolving x = e'cost, y = e'sint, 0 <t < about the x-axis,…

A: We’ll first need the derivatives of the parametric equations:

Q: Determine the element of surface area dS in the special case of the paraboloid of revolution z = x2…

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Q: Find the surface area of the solid of revolution obtained by rotating the curve 2y – y? from y = to…

A:

Q: Find the surface area of the surface resulting from revolving the cu y=x+2 on the interval [0,1]…

A:

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

A:

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: Compute the surface area of the cone generated by revolving the curve c(1) = (1, mt) about the…

A:

Q: Find the surface area of the paraboloid z = x² + y², 0 < z < 1. .

A: The surface is same as revolving the curve x2=z or x=z1/2, y=0 about z- axis. So surface area is:…

Q: 3. Find the area of the surface cut from the paraboloid x? + y +z = 2 by the plane y = 0.

A: Here we have to find the area of the surface cut from the paraboloid x2+y+z2=2 by the plane y=0.

Q: (b) Find the volume and the surface area of the truncated cone made by the rotation of the solid…

A: From the given graph: Now, from the graph given that:    r = 2 unit, R = 4 unit, and h = 3 unit.…

Q: 10. Use polar coordinates to find the volume of the solid under the surface z = (x² + y²)² and above…

A: The polar coordinate conversion is as follows x = r cos(θ) y = r sin(θ) x2 + y2 = r2 Under the…

Q: need ASAP B. Find the area of the portion of the cylindrical surface y = 4 − x2 in the first…

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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 exact area of the surface obtained x=t°, y =t 0<t<lby rotating about the x- аxis.

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.