A solid is formed by revolving the region bounded by the graph of f(x)= x^-p and the x-axis fro 0

Q: . The volume generated by revolving about the y-axis the region enclosed by the graphs y=9-x² and…

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Q: Find the area of the region bounded by the graph of f(x) = 2.x3 – 36x2 + 192x + 5 and the x-axis…

A: f'(x) = 6x2 -72x +192 (x-8)(x-4) =0

Q: Find the volume generated by revolving about the line y-2=0, the area bounded by x^2=8y and the line…

A: By using cylindrical shell & horizontal strip (Shell Method);The Volume of solid formed by…

Q: The region bounded by y=√(5-x), x=1, and y=0 is revolved around the (a) x-axis and the (b) y-axis.…

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Q: Find the volume of a solid bounded by y=(x2 -4) and y=(2x - x2) about the axis y=-4.

A: formula : here

Q: Find the volume of the resulting solid of revolution located in the first quadrant bounded by the…

A: According to question, Given curve, y=6x-x2

Q: Find the volume of the solid generated by rotating the region bounded by f(x) = 2-x², g(x)=√1-x², x…

A: We know The volume of the solid formed by revolving the region between curve fx and curve gx around…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y =2x + 1…

A: For the point of intersection of the curves, we will solve the given two curves as:…

Q: Find the volume of the region bounded above by the sur-face z = 9 - y2 and below by the rectangle R:…

A: our objective is to find the volume

Q: Find the volume of the region bounded by y=x^2 Below the x axis And on the right by the line x=3…

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Q: nded by y=25-x2 and y = 5. Limits from -4 to 4 x axis. Use washer

A: Consider the given curve as y=25-x2 and y=5

Q: Find the volume of the solid generated by rotating the region bounded by f(x) = 2 - x², g(x)=√1-x²,…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y 2x2 1 and…

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Q: Find the volume generated when the area bounded by the two curves of x2 = 4y and y2 = 4x is revolved…

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Q: Evaluate the volume of the surface of the shaped recreated by revolving the line y = 1/x as x goes…

A: Solution is written in below steps.

Q: 1.) Find the area bounded by the lines and curves y = 4x – x°, x =1 and x = 3

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: Determine the volume of revolution obtained by the region bounded by y = √√√x+3, y = √-x+3, y = 0…

A: We have to determine the volume of revolution obtained by the region bounded by y=x+3, y=−x+3, y=0…

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

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Q: Find the volume of the solid that results when the region in the first quadrant bounded by the curve…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: The region enclosed by the graph of the lines; y = lnx, y = 0,x = 0 and y = 1 is revolved about the…

A: The region is y=lnx, y=0 and x=0 and y=1 It is revolved about x=axis,  To find the volume of the…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y=2x + 1 and…

A: find intersection

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Given curves are

Q: The area bounded by the graphs of y = 2 - x^2 and y = x^2 revolves about the x-axis. Determine the…

A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…

Q: Find the volume of the solid generated by revolving the region bounded by the curve x2 y2 = 16 and…

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

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Q: Find the volume of a solid obtained by rotating the region underneath the graph of f(x)=64-4x^2…

A: Given query is to find the volume of the solid generated.

Q: Let R be the region bounded by the graphs of y = (x-1)^2-1 and 3x = y^2. Set up the sum of definite…

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Q: The base of a solid is the region bounded by the line y = 9 and the parabola y = x². Cuts…

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Q: Find the volume generated by revolving bout the line x = 3 the area bounded by (y - 2)* = -4(x - 4)…

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Q: Find the volume of the the solid formed by revolving the region bounded by y=5-x; y=0; about x-axis.…

A: Double integrating the region or integrating the area of a region gives the volume. Use proper…

Q: Compute for the volume of the solid formed bounded by the equations (y- 4)2 = x - 3, x-10, y-4, and…

A:

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: I am attaching image so that you understand each and every step.

Q: Find the volume of the solid that results when the region in the first quadrant bounded by the curve…

A: Find the volume of the solid that results when the region in the first quadrant bounded by the curve…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y = 2x + 1…

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Q: The region in the first quadrant bounded by the graph of y=8-x32, the x-axis, and the y-axis is…

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Q: Let RR be the first quadrant region bounded on the left by the yy-axis and between the graphs of…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: the volume of the solid obtained by revolving the graph of the function f(x) = 7x^5 on the interval…

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)=8x$ on the…

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Q: Sketch the area bounded by the function y = x^2 + 1 and the line y = 5, and then calculate the…

A: Volume of revolution

Q: Find the volume generated by rotating the region in the first quadrant bounded by y=exy=ex and the…

A: Consider the equation for x∈0, ln 3: y=ex……1

Q: Find the volume of the the solid formed by revolving the region bounded by the graphs of the…

A: option A is Correct

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)= 9x5 on the…

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Q: ) Find the surface area of the closed circular cylinder of greatest volume that can 5.(Total. be…

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Q: Find the volume of the solid formed by rotating the region bounded by y-3z+2, y- 3z+4, y - -3z+38…

A: Note: Dear subscriber, the third part of the solution is not done because of the complexity of the…

Q: Find the volume of region revolving about y axis, and bounded by x-axis and 0 < y < 2 y =

A: Given the curve y=x2is bounded by x axis. The region rotated about the y axis. Find the volume of…

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 8x³ on the…

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.