A solid is formed by revolving the region bounded by the graphs of y = 5x, y = In (r), y = 7, and the r-axis about the y-axis. Which of the following gives the volume of the solid?

Q: The volume of the solid generated by revolving the region by bounded 2 y = x + 1 , x = 2 and the y -…

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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: The graph of the volume for solid revolution between the curves y = x+1 and y = O around the x -…

A: Plot the lines and determine the area bounded by these lines. Use the area and the rotation about…

Q: The region between the curve y = 2/x and the x-axis from x = 1to x = 4 is revolved about the x-axis…

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the x…

Q: The base of a solid is the region in the first quadrant bounded by the graph of y =1- and the z- and…

A: Since each cross-section is perpendicular to the x-axis is a square, we have to find the area in…

Q: The base of a solid is the region between the curve, y2(p + x) = x²(3p – x), 0 < x < 3p, y 2 0 and…

A: Answer is written below

Q: The volume of the solid generated by revolving the region bounded by y = 2x - x² and (5a+1)π y = 0…

A: Volume

Q: Which solid has greater volume? Let R be the region in the first quadrant bounded by the graphs of x…

A: We first sketch the region using a graphing calculator. When this shaded region rotates about the…

Q: A region bounded by f(x) = 5 – x, y = 1, x = 1, and x = 3 is shown below. Find the volume of the…

A: The function of the curve is fx=5-x, y = 1, x = 1 and x= 3. The graph of the curve is shown above in…

Q: In the given question as follows, find the volume of the solid generated by revolving the region…

A: Definition used -                     Washer method -                     v=π∫ab(f2(x)-g2(x))dx…

Q: The base of a solid is the region between the curve, y (p +x) = x2(3p – x), 0 0 and the X – axis.…

A: Volume is a 3-dimensional quantity which describes the amount of space available inside the solid.…

Q: The area bounded by y = x² and y = 2 – x² is revolved about the x-axis. Find the volume of the solid…

A: We have to find volume of solid revolution.

Q: Let R be the region bounded by the graphs of y=x,x%39 and the x-axis, then the volume of the solid…

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Q: The volume of the solid obtained by rotating the region bounded by y=4-x, y=0, X=-2, x-2 about the…

A: Determine for true or false

Q: Consider the region bounded by the graph of y2 = (6 – x)2 (1 + x)2 on the interval [o, 1]. Find the…

A: Given: y2=6-x21+x2 To Find: The volume of the solid generated by revolving the region about the…

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: A region bounded by f(x) = x, y = 1, and x = 4 is shown below. Find the volume of the solid formed…

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Q: The region bounded by the graphs of x = 0, x = VIn y, and x = V2 - In y in the first quadrant is…

A: The region bounded by the graphs x=0, x=ln y and x=2-lny in the first quadrant.we have to find…

Q: 1. Find the volume of the solid generated when the region bounded by y = ex, x = 0, x = 2 and the…

A: Note: As per our guidelines we are instructed to solve only one problem. Hope you understand.    The…

Q: A region bounded by f(y) = y, y = 8, and x = 1 is shown below. Find the volume of the solid formed…

A: Given, f(y)=y3, y=8, x=1

Q: The base of a solid is the region bounded by y=cos(x) from x=0 to X= T/2. Find the volume of the…

A: L as the cross section generated are perpendicular to x-axis then area will be function of x donated…

Q: A region bounded by f(x) = x, y = 1, and x = 4 is shown below. Find the volume of the solid formed…

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Q: Consider the region bounded by the graphs of y = ln x, y = 0,and x = e. Find the volume of the solid…

A: To Determine: Consider the region bounded by the graphs of y = ln x, y = 0, and x = e. Find the…

Q: 2) ( ) Sketch and find the exact volume of the solid obtained by rotating the region B bounded by…

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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: 3. The base of a solid is a region bounded by the lines y = 2x−2 and y=−x+4 and the x- axis. If…

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Q: 19. Find the volume of the solid that results when the region enclosed by = 2y, y = 2, y = 3 and x =…

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Q: The region bounded by f(x) = - 3x? + 15x + 42, x = 0, and y O is rotated about the y-axis. Find the…

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Q: The region bounded by the curve y = x2 + 1 and the line y = −x + 3 is revolved about the x-axis to…

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Q: Consider the region bounded by the graphs of y = x√(16 − x2) , y = 0, x = 0, and x = 4. Find the…

A: Shell method: The volume of a solid generated by the region on [a, b] revolved about y axis is,…

Q: EXAMPLE The region between the curve y = Vx, 0 sxs 4, and the x-axis is revolved about the x-axis to…

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Q: For the region bounded by y=8-x^(3), the x-axis, and y-axis, determine which of the following is…

A: Lt's figure out the point of intersection.y = 8 – x3 = 0Hence, x = 2When x = 0; y = 8

Q: The region R in the first quadrant is bounded by y=(5x-4)^(1/2), y=0, y=4, and x=0 is revolved about…

A: Given,

Q: The solid formed when the region bounded by y=x, y=2x+ 2, x=2, and x=6 is revolved about the y-axis.…

A: Given the solid formed when the region bounded by y=x, y=2x+ 2, x=2, and x=6 is revolved about the…

Q: Find the exact volume of the solid whose region is bounded by y = 2 a + 2, y = 0, x = 3 and x =…

A: Given data : y=2x+2 , y=0x=3 , x=4

Q: The region between the curve y = 1/x2 and the x-axis from x = 1/2 to x = 2 is revolved about the…

A: Graph the given situation, shaded region is being rotated about y axis

Q: The volume of the solid obtained by rotating the region bounded by y-x, y-27 and x-0, y-0 about the…

A: To find the volume of the solid rotating the region about y axis.

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

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Q: What is the exact volume of a solid that is formed by rotating the region, enclosed by the functions…

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Q: The base of a solid is the region between the curve, y²(p +x) = x²(3p – x),0 0 and the X – axis. If…

A: Given, the base of a solid is the region between the curve, y2p+x=x23p-x, 0≤x≤3p, y≥0 and the…

Q: The region bounded by the curve y = x2 + 1 and the line y = 3 − x is revolved about the x-axis to…

A: Given that : The region bounded by the curve y = x2 + 1 and the line y = 3 − x is revolved about the…

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: Consider the region bounded by the graph of y2 = (4-x)^2/(1+x)^2 on the interval [0, 1]. Find the…

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Q: The region bounded by Y = LN(X), X = e, and the X axis is revolved about the Y axis. Use the shell…

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Q: Find the volume of the solid bounded above by the graph of x2 + y2 +z2 = 5 and below by the graph of…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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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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.