Q6. Calculate the volume of the solid obtained by rotating the region bounded by y = x ² – 4x + 5, x = 1, x = 4 and y = 0 about the X-axis.

Q: 1. Find the volume of the solid generated when the region bounded by y = 9- x² and y = 2x +6 is…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. Determine the volume of the solid obtained by rotating the region bounded by y = 4x and y = x³…

A: The volume of revolution of the area bounded by the curves y1=f1(x) and y2=f2(x)  between the limits…

Q: 2. Find the volume of the solid formed by revolving the region bounded by the graphs of x = -y² +…

A: Here we have given a solid region bounded byx=-y2+4y,y=1and x=0. So bounded solid region will be…

Q: Ex/ Find the volume of solid generated by revolving the region y2 and x = y enclosed by x = 1- about…

A: You have posted multiple question. As per the instruction, we will be answering the first question.…

Q: 4. (a) Find the volume of the solid generated when the region enclosed by y = -. 6-x2 and y = 0 is…

A: Given the solid generated when the region enclosed by  y=−6−x225  and  y=0   is revolved around the…

Q: b) By using the washer method, find the volume of solid obtained by revolving the region bounded by…

A: To find the volume of solid obtained by revolving the region bounded by y = 2x - 1 and y = x - 1…

Q: Find the volume of the solid obtained by rotating the region bounded by x = -6+ y² and a y about the…

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Q: Q1/ Find the volume of the solid generated by revolving the region bounded by y = Vcos x, y 0 & Osxs…

A: Disk method: The disk method is used to find the volume of a solid when the axis of revolution is…

Q: Q.5 Find the volume of the solid whose base is the region enclosed between the curve x=1-y and the…

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Q: 16. Find the volume of the solid generated by revolving the region enclosed by y = 3sinx and y = 0…

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Q: Q4/ Find the volume of the solid generated by revolving the region in the first quadrant bounded by…

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Q: 3. Find the volume of the solid of revolution when the region below y = x + 1 and between x = 0 and…

A: 3 We have to find the volume of the solid of revolution when the region below y=x+1 and between x=0…

Q: 14. Find the volume of the solid region generated by revolving the region bounded by y = 1-x² and y…

A: Here given, y=1-x2 and y=0, Then 1-x2=0⇒x2=1⇒x=±1

Q: 2. Find the volume oF solid obt ained by revolving the region bounded by the about the x- axis the…

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Q: 1) Calculate the volume of the solid created by rotating the region bounded by y = x² +1 y = -x + 3…

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Q: (#4) Find the volume of the solid bounded by y = 2x, y = 0, and x = 4 rotating on the x-axis:

A: Given a solid is bounded by the curves y=2x , y=0 and x=4 rotating on the x- axis.

Q: 4. Use the washer method to determine the volume of the solid obtained by the revolving the region…

A:

Q: 1) Find the volume formed by rotating the region enclosed by: x = 3y and y³ = x with y ≥ 0 about the…

A: answer is in next step . please give a like!!!

Q: Q2 ) Determine the volume of the solid obtained by rotating the portion of the region bounded by y =…

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Q: 3-Find the volume of the solid obtained by rotating the region bounded by y=2x+1, x=4 and y=3 about…

A: .

Q: Find the volume between the cylinders x+y =1 and the cylinder x* +z* = 1 in the first octant. 2

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Q: Q2/ Find the volume of the solid generated by revolving the region bounded by y = x² +1, y= x+3…

A: According to bartleby guidelines i can do only 1 question please reupload 2nd qstn

Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x + 4 and x - 2y + 4…

A: Given problem:- Calculate the volume of solid of revolution when the region bounded by y = √(x + 4)…

Q: What is the volume of the solid generated when the region bounded by the graph of x = √y - 2 and the…

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Q: 1. Find the volume of the solid generated when the region bounded by y = 9 - x? and y = 2x + 6 is…

A:

Q: Q2/ Find the volume of the solid generated by revolving the region bounded by y = x² +1, y = x+ 3…

A: Given Equation of parabola y=x2+1. Equation of line y=x+3.

Q: Q2 ) Determine the volume of the solid obtained by rotating the portion of the region bounded by y =…

A:

Q: and y=2 8) x = y² +1₁ x = 0, you, The most appropriate method to use to find the volume generated by…

A: The given region is x=y2+1,x=0,y=-1 and y=2. Find the volume generated by revolving the region about…

Q: 1. Find the volume of the solid generated when the region bounded by y = 9 – x² and y = 2x + 6 is…

A:

Q: 1. Find the volume of the solid of revolution generated by revolving the region bounded by y = x?…

A: Given problem:-  Find the volume of the solid of revolution generated by revolving the region…

Q: 1. Find the volume of the solid generated when the region bounded by y = 9-x2 and y = 2x + 6 is…

A: Given:       y=9-x2      y=2x+6 The volume for solid of revolution between curves is the volume of…

Q: Q2: Find the volume of the solid obtained by rotating the region bounded by y = x² + 3 and v = 1- x2…

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Q: Q3/ Find the volume of the solid generated by revolving the region bounded by y = 3/(2/x) , y = 0 &…

A: QUESTION 3

Q: Q5) Fid the volume of the solid generated by revolving the region between the curve y = x2 +1 and…

A: Volume

Q: 3) Find the volume of the of the solid that results when the region endosed by the curves y = Vx, y…

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

Q: 1- Find the volume of the solid obtained by rotating the region bounded by the curve y = 4 - r and…

A: The volume of the solid of the revolution of the curve y=f(x) obtained is  Volume=∫abA(x)dx  or…

Q: Q1/ Find the volume of the solid generated by revolving the region bounded by y = Vcos x, y = 0 &…

A: Given : y = cos x , y = 0 0 ≤ x ≤ π2   To find the volume of the solid generated by revolving the…

Q: 1. Use your preferred method to calculate the volume of the solid obtained by revolving the region…

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Q: 2. Consider the region bounded by the y-axis, y = 3x+ 1, and r 4. Find the volume of the solid…

A: Given function are y=3x+1x=4y axisAxis of rotation y=-5

Q: 4. Find the volume of the solid generated by revolving the region bounded by y = x 2 + 2 and y = x +…

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Q: Q5) 1- Find the volume of the solid generated by revolving the 2 region bounded by x = y+1 ,x = 0, y…

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Q: Q2|| Find the volume of the solid generated by revolving the region bounded by the curve -= X…

A: Volume of revolution

Q: 5. Find the volume of the solid obtained by rotating the region bounded by y = x³,y = 0, x = 1 about…

A:

Q: Q2/ Find the volume of the solid generated by revolving the region bounded by y = x² +1, y=x+3 about…

A: Given y=x2+1y=x+3

Q: 2. Find the volume of the solid generated by rotating the region bounded by y =÷x³ and %3D y = 6x -…

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Q: 2. Find the volume of the solid generated by revolving the region bounded by the y = ³, y= 0 and x =…

A: Find the volume of the solid generated by revolving the region bounded by the y=x3, y=0 and x=1…

Q: 5. Find the volume of the solid obtained by rotating the region bounded by y = x³,y = 0, x = 1 about…

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Q: Q2: Find the volume of the solid generated by revolving the region between the curve y = x and the…

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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.