The area S of the surface formed by revolving, about the x-axis, the region bounded by the graph of y =V9 - and the first quadrant is Select one: O a. None of these O b. S = S V81 – 522 dz Ocs- 6 V 81-5z O d.S - 27 zy9 -zdz

Q: HW: Find the area of the surface generaled by revolving 1. Vy , 1 <y58 about the x- axis. 3 2. y =…

A: Hello, thanks for your question but according to our policy I am answering the first three subparts.…

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A: According to question given that y=4-1x2y=0

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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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A: Given query is to find the volume generated when revolve the curves around y = 5.

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Q: (c) Given the curve C: y = Vx - 2 and the line L:x+y =4. Sketch the region bounded by the curve C,…

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Q: 4) Find the volume of the given solid: Under the surface z = 4y and above the region in the ry-plane…

A: We have to find the volume of the given solid:Under the surface z = 4y3 and above the regionin the…

Q: 1. Find the area bounded by the curves y?=2ax, y²=4ax-a? 2. By integration, show that the area of a…

A: As you have asked multiple questions so I have answered first question as per the guidelines

Q: бх and the x+1 In the figure below, R is the region bounded by the line x+y = 4, the curve y =-…

A: given functions are                                                  x+y=4y=6xx+1…

Q: Find volume the of gaphe the Solid the bounded L ty? =4, of Xty' +2= 16.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

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Q: 2.) y^2-8x-8y+8=0     a. Find the area bounded by this curve and its latus rectum

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A: Topic = volume

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Q: b) Find the volume of the solid obtained when the region under the curve y= 2-x , x=0,y%3D0 revolved…

A: We will find out the required volume of solid of revolution using cylindrical shell method.

Q: 3. Let R be the region bounded by the curves y = x2 +4 and y = 6x – x². Calculate the volume of the…

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Q: c) the volume of the solid found by rotating the region bounded by the given curves about the…

A:

Q: s. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A: According to question,  y = 1+ sec x,y = 3,and rotated about y =1.

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A: Graph:

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A: a)

Q: tind the volume V al the solid obtained by rotating the region bounded by the qiven curves about the…

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Q: 5. Find the volume of the solid that results when the region enclosed by the given curves is…

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Q: The area S of the surface formed by revolving, about the y-axis, the region bounded by the graph of…

A: We have to solve given problem:

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Q: The surface area of the surface generated by revolving y=x³ , 0<x<1 about the x- axis is S×3.56312…

A: Option 2 none

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A:

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x². If we revolve R about the line y =…

A: Above question is solved.

Q: A) If the volume (1) of the region (D) enclosed by the surfaces (z = x² + 3y²), and (z = 8 – x? –…

A: Answer A:   The intersection between surfaces: x2+3y2 = 8 - x2 - y2 2x2+4y2 = 8 x2+ 2y2 = 4 (x/2)2…

Q: The region R in the first quadrant is bounded by the coordinate axes, the curve y = e x = 4. and the…

A: Given: y=e-5x, x=4

Q: tind tre integ rol for the volcne of the solid obtoired by ro tading the y = the region bounded y yミ…

A:

Q: 3. Find the volume of the solid that results when the region enclosed by the given curves i revolved…

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Q: Q3) Find the volume of the solid generated by revolving region bounded by the curve (y=e* ) & the…

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Q: ー元 Q.3 Sketch the region enclosed by the curves y = sec' x, y=x² +1, xr=- 4 and find 4. its area.

A: Sketch the region and integrate the function with x from -π/4 to π/4.

Q: Find the volume of the solid of revolution when the region bounded by the line y=x+2 and the curve…

A: The volume for solid of revolution between curves is the volume of object between a curve y=fx and 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.