Find the volume generated if the area of the region bounded by y= 1/x, y=x/4 and x=3 is revolved about the line x=-5

Q: y2- 4y + 2x = 0, x = 2 and x-axis

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Q: Consider the region formed by the graphs of f (x)=sqrt( x) , f (x)= 1/x and x = 2. Set up the…

A: We sketch the region using a graphing calculator.  Red curve is : y=1/x Violet curve is: y=sqrt(x)…

Q: Consider the region formed by the graphs of f (x)=sqrt( x) , f (x)= (1 /x)and x = 2. set up the…

A: We sketch the region using a graphing calculator. Violet curve is: f(x)=sqrt(x) Black curve is:…

Q: Find the volume obtained by rotating the bounded region defined by y = Vx y = 0 , and x = 4 around…

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Q: Find the volume of the solid obtained by revolving the region bounded by the graph of f(x) = 8e-lx,…

A: Given the curves: fx=8e-7x, x axis, y axis, x =6rotated about y axis

Q: Find the volume generated by revolving about the x-axis the regions bounded by the following graphs.…

A: Given that         y = ex  , x=-2 , x=1  Here we have to find the volume generated by revolving…

Q: The best method applicable to find the volume of the region bounded by x = y? and x = 2+y revolved…

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Q: Find the volume bounded by: x² + y² + z = 16 and z-x² - y² = 8

A: Concept: If a solid S is bounded by a surface, as in rectangular coordinates,  z=f(r,θ) as well as…

Q: Find the volume obtained if the figure formed when the region bounded by y=x^2 and y = 2x is rotated…

A: NOTE: Refresh your page if you can't see any equations. . here have to find the intersection…

Q: What is the volume obtained by rotating the region bounded by x = (y - 3)½ and y = 2x2 + 1 around…

A: Here we use basic definition of volume .

Q: The volume generated by revolving the area bounded by the curve y = x² and y = 4 around the line y =…

A: We can use the formula π∫abR(x)2dx to evaluate the volume.

Q: Find the volume generated by the region bounded by - y = z, z= 0 and y = 1 when it is revolved about…

A: The region is bounded by y2=x , x=0 and y=1 as :-

Q: 4. Find the volume of the region bounded by y = -x+1, x = 0 and y = 0 revolved about the x-axis.

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Q: Find the volume of the solid generated when the region bounded by y = x² – x and y = x - y2 is…

A: Introduction: If the area of the ring is A=πOuter radius2-(Inner radius)2, the volume of solid…

Q: Find the volume generated if the area bounded by the curve x2 = y - 2 is revolved about the x –…

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Q: Find the volume generated if the area bounded by the curve x² = y – 2 is revolved about the x-axis.

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Q: Compute the volume generated by the curve = 4 y = z about x-axis between x = 2 and x x2

A: Given curve is  revolved around x-axis ,so now we will find volume generated by intigration between…

Q: Find the volume of the solid generated when the region bounded by y = 9x and y = 36/x is revolved…

A: The given curves fx=36xgx=9x Solving the above equation 36x=9x362x-81x2=0x362-81x=0x=0, 16

Q: What is the volume (in πcu. units) of the region bounded by the curve y=x^3, and the lines x=1, x=2…

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Q: Find the volume of the sold generated by revolving the specified region about the given line. R…

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Q: 4. Find the volume of the region bounded by y = - x+1, x = 0 and y = 0 revolved about the x-axis.

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Q: Find the volume generated if the area bounded by curve y=x^2 and the line y=2x + 3 is revolved about…

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Q: ut the line x = 3.

A: The parabola equation is given , x2 = 4y. The equation of line is given , x = 4 - 2y. The volume…

Q: Find the volume formed by revolving about the x-axis the area bounded by the curve (x + 1)^2 = 4(x -…

A: Given data:- Equation of curve, x+12=4x-1 Line, y=4

Q: Find the volume (in cubic units) of the region bounded by the curves y= Sin x ,and y= cos x and the…

A: The solution are next step

Q: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine the…

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Q: Find the volume generated when the area bounded by the two curves of x^2 = 4y and y^2 = 4x is…

A: We will find out volume of solid of revolution.

Q: Find the volume of the solid obtained if the region bounded by the graphs of y = \x , y =0, and x=9…

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

Q: Find the volume of: the area bounded by the curve y2 = 9x and the line x = 4 revolved about x = 4.

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Q: Find the volume generated by rotating the region between the graphs of y = 2 - x, x = 0, and the…

A: Consider the provided region, y=2-x,x=0 Find the volume generated by rotating the region between the…

Q: Find the volume generated by revolving the area bounded by xy=4, x=1, x=4 and the x-axis about the…

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Q: Compute the volume bounded by y=x²-2x and 3y +2x²-27=0 when it is revolved around the y-axis

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Q: Find the volume generated by the region bounded by the curve y 12X and the line X3 rotated about the…

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Q: Find the volume generated by the area bounded by the y-axis, the line y=1, and the arc of y=sin x…

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Q: Find the volume generated by revolving about the line 0x the area bounded by the curve 1 (포2 - 1)…

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Q: Find the volume of the region bounded by: x y +1 that is rotated about the x-axis.

A: Use volume formula about x axis

Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: Find the volume (in cubic units) of the region bounded by the curves y' = 4x and the line X = y when…

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Q: Find the volume of the region formed by revolving the region bounded by y=sqrt x, y=0, and x=4 about…

A: First, we sketch the region using a graphing calculator  The shaded region is rotating about the…

Q: find the volume “V” obtained by revolutionizing the region between y=x2  and y=12-x around the axis…

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Q: Find the volume of the solid obtained by rotating the region bounded by x = 8 – y² - and x 2y about…

A: Given the region is bounded by the curves x=2y and x=8-y2 about the line x=9. The curves intersect…

Q: Determine the volume generated when the area bounded by the curves y-sinx and y=cosx from x=0 to…

A: Solution :-

Q: Determine the volume produced by the region bordered by x² - 4x - 4y + 4 = 0 and y = 1 about the…

A: We will use disk method to find volume of solid generated

Q: The area bound by the curve y^2 = 12x and the line x = 3 is revolved about the line x = 3. What is…

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Q: Find the volume generated by revolving about the x – axis the area bounded by y^2=4x and x^2=4y

A: The volume generated by revolving the area bounded by the curves fx and gx is V=∫abπfx2−gx2dx. The…

Q: Find the volume generated by revolving the area bounded by   xy=4, x=1, x=4 and the x-axis about the…

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Q: Find the volume if the region bounded above x axis is rotated about the x axis

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

Q: Solids of Revolution ( refer to the image )

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Q: Find the exact volume generated by revolving the region bounded by f(x) = 2x^2 + 10 and g(x) = 4x +…

A: The volume generated by revolving the region by line y= 10 The given functions are fx=2x2+10 and…

Q: Find the volume formed by revolving the region about the line x = 4. 1 2 3 y = 3 – x & y = -x² + 2x…

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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.