In the following diagram, the points A and B lie on a circle centred at the origin, and are connected by a line segment. B = (0,5) The shaded region, between the line A = (-4,3) segment ana tne quarter-circle, rotates about the x-axis. Find the volume of the 2 resulting solid. Show your work. -6 -5 -4 -3 -2

Q: Determine the volume of the rotating object that occurs if the area of ​​the curve y1 = - x2 + 4 and…

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Q: The region enclosed by the x-axis and the parabola y = ƒ(x) = 3x - x2is revolved about the vertical…

A: Here we have to evaluate the Volume of the solid,  bounded by the x-axis and parabola y=f(x) = 3x-x2…

Q: 2) Find the volume of the solid enclosed be+ween the Z = 5x2+ 5y? and Z = 6-7x* -y².

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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: The volume generated by revolving the first-quadrant area bounded by the parabola y2 = 8x and the…

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Q: find the volume generated of the area bounded by x^2 = ay, the x-axis and x = b which is revolved…

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Q: Find the volume of the figure formed by the revolution about the given axis. (0, 0), (2, 4), & (6,…

A: Here we find the volume by revolution around x-axis

Q: Find the volume of the torus generated by revolving the circle (x - 2)^2 + y^2 = 1 about the y-axis.

A: Given: (x-2)2+y2=1

Q: Find the volume of the torus formed by revolving the circle x2 + y2 = a2 about the line x = b(b >…

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Q: Q3: Find the volume of the solid enclosed by the parabola y = x? + 22 and the coney = 32 — x? — z2,

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Q: For y = x3-7x2+15x-9 from x=1 and x=2 and above the x-axis, find the volume that results from…

A: The volume of the solid can be calculated by using the following formula.

Q: Given the area in the first quadrant bound by x²= 8y , the line x= 3 and the x-axis. What is the…

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Q: Find the volume of the torus generated by revolving the circle (x−5)2+y2=4 about the​ y-axis. What…

A: Here, equation of circle is: (x-5)2+y2=4 So, the centre of the circle is (5,0) and radius will be 2.…

Q: nd the volume of the solid generated by

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Q: The circle x2 + y2 = a2 is rotated about the x-axis to generate a sphere. Find its volume.

A: we have been given that the circle x2 + y2 = a2 is rotated about the x-axis to generate a sphere. we…

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

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Q: Find the volume limited by the graphs of the equations

A: Part (a):

Q: The base of a solid is the region bounded by the ellipse 4x² + 9y? 36. Find %3D the volume of the…

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Q: Find the volume of the solid that results when the shaded region is 5 revolved about the indicated…

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Q: Q3: Find the volume of the solid enclosed by the parabola y = x² +z? and the cone y = 32 – x² - z2.

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Q: 8. 9. 2- -5 5. 10 -2-

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Q: For each problem, find the volume of the solid that results when the region enclosed by the curves…

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Q: Find the volume of the solid that results when the shaded region is 7 revolved about the indicated…

A: Use the washer method to find the volume of rotation of the solid.

Q: The base of a solid is the region in the first quadrant between the graph of y = x and the x-axis…

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Q: (c) Suppose each cross section perpendicular to the x-axis is an isosceles right triangle with one…

A: Note: There are multiple questions. Few questions has multiple subparts. No specific question has…

Q: The region bounded by y = 3x - 9 andy = -3x2 + 18 x - 9 revolved about the y-axis. Find the volume…

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Q: The base of a solid is the region in the first quadrant bounded by the graph of y=2x-x^2 and the…

A: *to find:- Volume of solid.

Q: 54. Look for the volume of the solid produced by rotating the region enclosed by 1792# T y - x² =…

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

A: Given-  To Find- The volume of the solid that is rotated about the indicated axis.

Q: Find the volume of the solid that results when the shaded region is 7 revolved about the indicated…

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Q: Find the volume of the solid that results when the shaded region is 7 revolved about the indicated…

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

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Q: Find the volume of the solid that results when the shaded region is 3 revolved about the indicated…

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Q: Find the volume generated by a parabola y2=4(51)x, its axis and its latus rectum revolves around its…

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Q: +v² , but outside Find the volume of the solid in the first octant under the upside-down cone :=6-…

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Q: 2Ay-3-2r

A: In this question we find volume of the shaded region that is revolved arround y-axis.     Here i…

Q: The vertices of a triangle are at (0,0), (6,6), and (9,3) . What is the volume, in cubic units, of…

A: The figure by hand is show below of the given question:

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: %3D y = 4-2r %3D D R.

A: Since, the prism is - D=x,y,z0≤x≤2,0≤y≤4-2x,0≤z≤6or0≤x≤4-y2,0≤y≤4,0≤z≤6

Q: Find the volume of the solid generated by revolving area of a circle: (x-2)²+y²=4

A: Rotate the circle:By rotating the circle around the y-axis, wegenerate a solid of revolution called…

Q: Find the volume of the solid that results when the shaded region is 6 revolved about the indicated…

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Q: By Sketching the graph, find the volume of the solid generated by revolving the region given by, y =…

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Q: What is the volume of the torus whose region is inside the circle

A: (x-3)2 + y2 = 1. Take it as the form (x-b)2 + y2 = a2, where b=3 and a=1.

Q: 6. Find the volume of the torus generated by revolving the circle x² + y² = 4 about the line .x = 3.

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

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Q: Q3 By sketching the graph, find the volume of the solid generated by revolving the region bounded by…

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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: Determine the volume V and total surface area A of the solid generated by revolving the area shown…

A: The area of the cross section is computed as follows, The cross section contains half circle and…

Q: y = x y=2-x2

A: The region is bounded by the curves y=2-x2 and y=x is rotated about x-axis. we have to fins the…

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.