Find the volume of the solid obtained by rotating the region bounded by x = 3 - y and x = -2y about the line x = 9. Round to the nearest thousandth. 10 8. 6. -10 -8 -6 -4 4 9. 10 -6 -8 -10

Q: (9) Find the volume when the region bounded by the curves y= e, x=-1, x=1, and the x-axis is rotated…

A: Given y=ex2, x=-1, x=1 and the x-axis is rotated about the y-axis.

Q: Let D be the region enclosed by y = 2x + 1, y = 2x + 3, x = 0 and x = 6. The volume of the solid…

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

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Q: Find the volume of the solid obtained by rotating the region between the curves y = 3x - x³ and…

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Q: Find the area of the region bounded by the curves y = 2x^2 − 8x + 12 and y = −2x + 12.

A: Answer

Q: 1) Find the volume of the solid cut from the first octant by the surface z=4-x2-y.

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

Q: 9. Find the volume of the solid whose base is the region enclosed by y = 2 –- x² and the x-axis and…

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Q: 4) Which integral expression shows the volume of that results when the region enclosed by y 2-2x, y…

A: Given that y=2-2x, y=0 So, the one function is y=2+1-2x=3-2x. The general formula for volume is,…

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

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Q: The solid S has a base described by the circle x² + y² = 1. Cross sections perpendicular to the…

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Q: Find the volume of the region that is between x = 8 – z2 – y? and x = -V4y² + 4z²

A: b)the region bounded by surface x=8-y2-z2andx=-4y2+4z2inside the disky2+z2=4

Q: If x > 0, find the volume of the solid obtained by rotating the region enclosed by the graphs about…

A: Wed use washer method to find volume about y=-8

Q: 11. Find the volume of the a 3-dimensional solid whose base is given below and whose cross sections…

A: TO FIND THE VOLUME OF SOLID GIVEN BELOW FORMED BY THE CURVES  y=4-x2 ; y=0 ;x=0 by using the concept…

Q: 31. Use the trapezoidal rule with n= 7 to estimate the volume of the solid generated by rotating the…

A: We know that; The expression for the volume of the revolution about the x-axis is: V=∫abπy2dx Given:…

Q: What is the volume of the region bounded by the lines f (x) = x², x = 1, and y = 5 rotated about…

A: The given region is: y=x2,  x=1,  y=5

Q: What is the exact volume of a solid that is formed by rotating the function h (x) = 4/x about the…

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Q: Determine the volume of the solid formed by revolving the area bounded by 4y=x³, y=0 and x=2 about…

A: We need to find volume.

Q: What is the volume of the region bounded by the lines f (x) = 3x², x = v2, and y = 10 rotated about…

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

A:

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

A: A solid is formed by revolving the region bounded by the graph of f(x) = x−p and the x axis for 0…

Q: The base of a solid is the region enclosed by the graph of y = vln x, the line x = e, and the…

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Q: 6. Find the volume of a solid whose base is the region bounded by y = 4 – x² and the x-axis and…

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Q: The region in the first quadrant that is bounded above by the curve y = 1/sqrt(x), on the left by…

A: Given,

Q: What is the exact volume of a solid that is formed by rotating the function h (x) = 6/x about the…

A: Explained below...

Q: Consider the region in the First Quadrant bounded by y = 1/x and y = x^2 from x = 1 to x =2. Find…

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

Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x2 = 8y,…

A:

Q: Find the volume of the region inside both z2 + 4 = x² + y² and x2 + y? + z2 = 16.

A: Given that, z2+4=x2+y2, x2+y2+z2=16 Intersection of both curve is, x2+y2+x2+y2-4=16x2+y2=10 So the…

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

A:

Q: 4. Compute for the volume of the solid formed by rotating the shaded area about the x- axis. * 30-…

A: Given: f(x)=25-x2

Q: 23. The region bounded by the curve 4y = x, the line x = 4 and the line y = 1, is rotated through…

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

Q: The region in the first quadrant that is bounded above by the curve y = 1/x^(1/4), on the left by…

A: Graph the situation using graphing calculatorWe have to rotate the shaded region.

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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 obtained by rotating the region bounded by x = 2 – y? and x = y about…

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

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Q: The volume of a right circular cone with radius r and height h is V=πr2h/3.   a. Approximate the…

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Q: What is the exact volume of a solid that is formed by rotating the function h (x) =7/x about the –…

A: As we know that; The expression for the volume of solid rotating about the x-axis is: V=∫x1x2πhx2dx…

Q: 2. Approximate the change in the volume of a sphere when its radius changes from r = 5ft to r =…

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Q: Use the Midpoint Rule with n = 5 to estimate the volume V obtained by rotating about the y-axis the…

A: The graph will be

Q: 2. Find the volume of the region common to the cylinders r2 + y² = 9 and z2 + z² = 9.

A: USING  FORMULA VOLUME =8∫∫∫dxdydz

Q: 6. Find the volume if the area bounded by the curve y = x3 + 1, the x-axis and the limits of x = 0…

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Q: 4. The area bounded by the parabola ay = x", the x-axis, and the line x = b isrevolved about the…

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Q: d the volume of losed by y = line

A: Here the function is f(x)=x , y=0 and x=9  is revolved about the line x=9

Q: 18. Find the volume of the solid obtained by revolving the region under the graph of y = 5- on [1,…

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Q: Compute the ”volume” of the 4-dimensional unit ball, which is the area enclosed by the equation x^2…

A: Given that, x2+y2+z2+w2=1. The volume for n dimensional unit ball is, V(n)=V(n-2)×2πn For n=4,…

Q: se the Shell Method to compute the volume of the solid obtained by rotating the region above the…

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

A: The answer is found in step-2

Q: What is the exact volume of a solid that is formed by rotating the function g(x) = 3x2 + 4 about the…

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Q: 1) The region between the graph of f(x) = Vx In x and the x-axis, for 1 <x < e°, is revolved about…

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Q: 2. Find the volume of the solid that results when the shaded region is revolved about the indicated…

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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.