Compute for the volume of the solid revolution formed. The area bounded by y=sinx, the x-axis, and the lines x= π/2 and x=2π rotated about x-axis.

Q: Consider the region R bounded by the line y = 33 - 5x and the parabola y = 27 – x2. To find the…

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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: 5. Find the volume of the solid obtained by rotating about the x - axis of the region bounded by y =…

A: We have to compute the volume of the solid generated by revolving the region bounded by the curve…

Q: Find the volume of the solid of revolution formed by rotating the region bounded by the parabola…

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Q: Find the volume of the solid S generated if the region is bounded by y = sec x, the x - axis, the…

A: Given:    Region y=secx line x=π4  Volume of solid V=π∫abfx2dx   here f(x)=secx            a=0…

Q: Draw the area bounded by the function y = x^2 + 1 and the line y = 2, and then calculate the volume…

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Q: Find the volume of the solid obtained by rotating the region bounded by 2y about the line x = – x =…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 26. x = 4 - y, x = 16- y?

A: Given that x=4-y, x=16-y2  To find the volume about line y axis.     Formulas used: Volume of…

Q: 2. Solve for the volume of solid of revolution formed by rotating the area bounded by y = x² + 2, x…

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Q: 3. Find the volume of the solid generated when the region enclosed by y = v2x + 8, y = x, x = 0 is…

A: Given

Q: Calculate the volume V of the solid obtained by rotating the region under y = x2 about the x-axis…

A: To find the volume V of the solid obtained by rotating under a region, use the formula, V=∫abπ(y)2dx…

Q: Find the volume of the solid of revolution bounded by y = 1/(x+1), x = 0, x = 2, and the x-axis, and…

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Q: Find the volume of the region between the cylinders x² + y² = 36 and x? + z2 = 36.

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Q: Find the volume of the solid generated when the region enclosed by y = √ x, y = 2, and x = 0 is…

A: Given: y = x, y = 2,  x = 0 To find: The volume of the solid generated when the region enclosed by y…

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

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Q: For the region bounded by the curves y = 2v/x, and y = 2 x2, find the following: 1. The area of the…

A: Area and volume

Q: 10. Find the volume of the solid obtained by rotating the region bounded by y = x³. x = 0, and x = 1…

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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: Find the volume of the solid region in the first octant inside the cylinder x²+y2=4 and between the…

A: Introduction: Finding a function's anti-derivatives is made easier with the aid of integral…

Q: 4.Find the volume of the solid that is obtained by rotating the region bounded by y = /x +1, y = Vx…

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Q: Find the volume of the solid obtained by rotating the region bounded by a. y = V25 – x2 and y = 0…

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Q: Find the volume oF the solid obtained by rotating about the x-axis the region by y= x' and the lines…

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Q: 3. Find the volume of the solid whose base is the region in the first quadrant between the curve y=…

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Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y = x°, y =…

A: We have to determine volumes of solid

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves

A: We have two given curves : y=x+1  and y=0 We have to find the volume V of the solid obtained by…

Q: 9. Find the volume of the solid obtained by rotating the region bounded by y = Vx. x 0, and x = 4…

A: To find: The volume of the solid obtain by rotating the region bounded by y=x, x=0 and x=4 about the…

Q: Find the volume of the solid whose base is the region enclosed by y=x^2 and y=4, and the cross…

A: Given: Region enclosed by y=x^2 and y=4. And the cross sections perpendicular to the y-axis are…

Q: 2. Find the volume of the solid generated when the region between y = sin x and y = 0 for 0 ≤ x ≤ π…

A: The region between y=sin x and y=0 for 0≤x≤π is revolved about the y-axis.

Q: Find the volumes of the solids generated by revolving the region between y = 4Vx and y about a) the…

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

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Q: 1. Find the volume of a solid if the area boun ded by the curve y = In x, the x-axis and the line x…

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Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-4x+5, x=4, and…

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Q: Find the volume of the solid of revolution when the region bounded by y = x + 1, the x – axis, and…

A: Recall: Shell method,  V=2π∫abr(x)h(x)dx We have, a=0, b=2, r(x)=3-x, h(x)=x+1

Q: What is the volume formed by revolving about the x-axis the area bounded by the lines x = 1, x = 5…

A: the volume (V) formed by revolving the curve y=f(x) about the x-axis bounded by x=a, x=b (b>a) is…

Q: Set up the equation in solving volume of the solid generated when the area bounded by a = √√√y, x =…

A: Given that,

Q: The area bounded by y = x3 + 2x + 1, x = 1 and x = 3 is to be revolved about the x-axis. Find the…

A: Given problem:- The area bounded by y = x3 + 2x + 1, x = 1 and x = 3 is to be revolved about the…

Q: Let a> 1 be a constant and let R be the region bounded by y= 6x² and y = 6x + 12 . Find the volume…

A: Given: Region bounded by y = 6x2 and y=6x+12 To find: volume of solid generated  by revolving region…

Q: Find the volume of the solid obtained by rotating the region enclosed by the curves f(x)=x^2+8 and…

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Q: (c) Compute the volume of the solid of revolution of R about the y axis.

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Q: Let a> 1 be a constant and let R be the region bounded by y = 10x² and y = 10x + 20 . Find the…

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Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = 3/T,…

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Q: Solve for the volume of the solid generated by revolving about the y-axis the area under y x = 4 to…

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Q: Find the volume of the solid whose base is the region enclosed by y=x^2 and y=1, and the cross…

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Q: Find the volume of the solid formed by rotating the region enclosed by y = el + 5, y = 0, x = 0, x =…

A: We have to find volume

Q: For the region bounded by the curves y = x2 + 1 and y = 3 – x², find the following: 1. The area of…

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Q: 2. Find the volume for the solid generated by taking the area enclosed by f(x)=cos(x), x=0, x = and…

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Q: B. Find the volume of the solid generated when the plane region bounded by 3. y = e-x² and the x –…

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Q: for the region bounded by y=3x, the x-axis, and x=1, determine which of the following is greater:…

A: Given

Q: 1. Sketch the region enclosed by the curves of y = x² – 2x. y=x+4, x =-2, x = 5 and find the area of…

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Q: Find the volume of the solid that results when the region bounded by x = y and x = 3y + 10 is…

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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.