10 1 -2 The graph above shows the base of an object. Compute the exact value of the volume of the object, given that cross sections (perpendicular to the base) are equiangular triangles. V =

Q: 5. Find the volume of the solid generated by revolving the area of a circle: (x - 2)² + y² = 4;…

A: In this question, we need to find the volume of solid generated by revolving the area of the given…

Q: 10. Find the volume of the largest right cone that fits in the sphere of radium 1.

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Q: If the area bounded by y = x² and y = 2 – x² is revolved about the x – axis and a vertical…

A: We have to find the volume of the solid if the area bounded by y=x2 and y=2-x2 is revolved about the…

Q: Suppose that R is the finite region bounded by y = 1, y = x + 5, x = 0, and z = 4. Find the exact…

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Q: A volume is described as follows: 1. the base is the region bounded by æ = – y² + 2y + 98 and æ 2.…

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Q: The region bounded by y = 0 and y = kx – x is revolved around the y-axis to form a solic whose…

A: Given,        y=0, and  y=kx-x2

Q: 3 14. Find the volume of the solid that results when the region bound by y = x°, x = 2 and the…

A: The given region is the region bounded by y=x3,x-axis y=0 and x=2. To find the volume when the…

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

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Q: A volume is described as follows: 1.  the base is the region bounded by x=−y^2+10y+93 and…

A: The base of the object is the region bounded by x=−y2+10y+93 and x=y2−30y+243 Every cross-section…

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

A: The curves are given by,

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: 4. Find the volume of the solid generated by revolving the region enclosed by the graphs of y = e* ,…

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Q: For a right circular cylinder, suppose that r = 6 in and H - 7 in. Find the exact:Total area,…

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Q: Suppose that RR is the finite region bounded by  y=x, y=x+4, x=0, and x=2. Find the exact value of…

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Q: Given the region bounded by y=×^3 ,X = 2, and the x-axis (in Quadrant I) is rotated about the line y…

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Q: A volume is described as follows: 1. the base is the region bounded by x 2. every cross section…

A: Given that the base is the region bounded by x=-y2+16y+182 and x=y2-26y+182 and every cross section…

Q: The base of the solid S is the region enclosed by the graph of y=sqrtln(x), the line x=e and the…

A: Given The base of the solid S is the region enclosed by the graph of y=sqrtln(x), the line x=e and…

Q: 3. If the region bounded by the curves y =x, y=0, and x =9 is the base of a solid, and cross…

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Q: he region bounded by y = e, y = 0, x = 0, and x = 1 is revolved about the y- xis. Find the volume of…

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Q: 1- Use the shell method to find the volume of the solids generated by revolving the shaded region…

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Q: 5. Ay 1 y = ycos x π 4.

A: Apply the washer method; The volume of revolution of the curve about x-axis, from x = a to x = b is…

Q: What is the exact volume of a solid that is formed by rotating the region ,2 bound by g (x) = x + 4,…

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Q: 4 5 6 7 9 1 -2 The graph above shows the base of an object. Compute the exact value of the volume of…

A: Consider the following diagram showing one slice of the solid formed above the given base: The base…

Q: 1. Find the volume of the solid that results when the shaded region is revolved about the X - AXIS.…

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Q: 14. Find the volume tended by the graph of f(x, y) = 1+2x + 3y, the rectangle [1, 2] x [0, 1], and…

A: Given function is: fx,y=1+2x+3y and the coordinate of the rectangle is: 1,2×0,1

Q: A volume is described as follows: 1. the base is the region bounded by - y' + 4y + 147 and 2 x = y –…

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Q: The base of a solid is the region between the curve, y 2 (p + x) = x 2 (3p - x), 0 0 and the X- axis…

A: Given: The base of a solid is the region between the curve y2(p+x)=x2(3p-x), 0≤x≤3p, y≥0 and the…

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: This question is designed to be answered with a calculator. The region bounded by y = x - 3x and y =…

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Q: Suppose that R is the finite region bounded by y = x, y = x + 2, a = 0, and a 3. Find the exact…

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Q: Match the volume formula(s) on the right to the appropriate geometric solid on the left. Some solids…

A: In the question we have to mark correct option for volume of given shapes.

Q: Suppose that R is the finite region bounded by y = x, y = x + 5, x = 0, and x = = 4. Find the exact…

A: Find the required Volume of oABC

Q: Find the volume.

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Q: Suppose that R is the finite region bounded by y = x, y = x + 1, x = 0, and x = 5. Find the exact…

A: In the Given Problem we have to find Volume bounded by  y=x , y=x+1 , x=0 and x=5 about x-axis   As…

Q: Given the region bounded by y= x^3 ,x = 2, and the x-axis (in Quadrant I) is rotated about the line…

A: Given problem:- Given the region bounded by y=x3 ,X = 2, and the x-axis (in Quadrant I) is rotated…

Q: 31 Find the volume of the solid generated by rotating the shaded region R through 360° about the…

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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: 2. Find the largest volume of a cylinder that fits into a cone has base radium R and height

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Q: Given:  The region is bounded by the curve y=4x-x^2, y=4 and the y-axis Problem : The volume…

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Q: 7. 3. x = V1 +y

A: Topic = Volume

Q: 3. Find the volume of the region common to the interiors of cylinders a? + y² = 1 and r? + z2 = 1

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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: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ =…

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Q: Find the volume of the solid in the Ist quadrant under the graph of z= f(2, y) = 3- VP+y² and inside…

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Q: find vołume 29. The region common to the interiors of the cylinders x? + y² = 1 and x? + z? = 1,…

A: Given: The region is given in the following diagram, The volume of the region is calculated as…

Q: 4. Find the volume of the solid that lies above the cone o H and below the sphere p = 2.

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Q: 15. Find the volume by the parabole y² = of the solid generated by revolving y-axis, the area…

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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: 4. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and…

A: Please see the attached picture on the white board.The shaded region in the top figure is the…

Q: 1 The volume of a right circular cone of radius æ and height y is given by V = ÷ Taʼy. Suppose that…

A: Rewrite the formula for volume and substitute the numerical value of V. Rearrange the equation, so…

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.