find The Volume of body resLt from Volating The are- between s- Sillx` alnd The Line X= about -axis.

Q: Find the volume of the region that is formed by revolving the function y = cos x bounded by the…

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Q: Find the volume of the solid obtained by revolving the region bounded by the graph of f (x) = 2/x…

A: Please refer the attached image for complete solution.

Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (x - 2)2 = 4(y + 2)…

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Q: Use differential to approximate the change in the volume of a sphere when its radius changes from 2…

A: Use differentials to approximate the change in the volume of a sphere when the radius is increased…

Q: Find the volume of solid generated when area bounded

A: Given: The area bounded by  y=x2 and y=x is revolve about x=2.

Q: A region in the first quadrant is bounded above by the curve y=cosh(x), below by the curve y =…

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Q: The volume for solid of revolution between the curves y = √49-x² and y=0 around the x-axis is (26/3)…

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Q: The area bounded by the y-axis, the line y = 1 and that arc of y = sinx between x = 0 and x = 1/2 is…

A: The given region is: y-axis,   y=1,  and the arc  y=sin x      between   x=0  to  x=π2

Q: The area bounded by the lines x = 0, x = 2, x + y = 4, and x – y = 4 is revolved about  the line x =…

A: Given problem:- The area bounded by the lines x = 0, x = 2, x + y = 4, and x – y = 4 is revolved…

Q: Find the volume V of the solid obtained by revolving about the line y = - 4 the region between the…

A: Obtain the volume with the help of Washers method.

Q: Find the volume of The region R bounded by the graph of y=4sinx and the​ x-axis on [0, π] is…

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Q: Find the volume of revolution of the region bounded by the curves x = (y-2)½, y = x + 4, and y-axis…

A: Plot the graphs:

Q: 8. The area bounded by the curve y = (x² – 2)? and the x-axis is revolved about the line x = 4. Find…

A: The volume of the solid of the revolution can be calculated using the shell method. The formula for…

Q: The area bounded by y^2 + x - y = 1, y-axis, and the line 2y = 9 is revolved about the line x = 1…

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Q: The region in the first quadrant that is bounded above by the curve y = ex - 1, below by the x-axis,…

A: Express the integral as below.

Q: The area bounded by the curve y^2 = 4x and the line 2x -y = 12 is revolved about the y-axis. Find…

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Q: Q2/ The region bounded by the curve y = x² and the line y = 3x, in the first quadrant is revolved…

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Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (x – 2)² = 4()y + 2)…

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Q: Find the volume generated by revolving the area bounded by the curve y = (1 − x2)2 and the x-axis…

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Q: Use differential to calculate the volume of the material needed in making a thin sphere with inner…

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Q: The region bounded by the parabola y = x and the line y = 2x is revolved about the line y = -1. Find…

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Q: The volume produced by revolving about the x-axis the region above the curve y= x° below the line y…

A: To find  The volume produced by revolving about the X-axis the region above the curve and below the…

Q: Find the volume generated by revolving about the line x=0 the area bounded by the curve y^(1/2) =…

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Q: Determine: a) Differential Area (dA) b) bar X (x with line on top) c) bar Y (y with line on top)…

A: The x-coordinate of the centroid of a triangle can be obtained using the expression x=∫xdA∫dA. The…

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: ind the volume generated by revolving the area enclosed by the curve x²+y²=25 about the line y-8=0.

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Q: Find the volume generated by revolving about the y-axis the area bounded by the curve x2 = 4(x-y),…

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Q: Find the volume generated by revolving bout the line x -1 the area bounded by (y + 2) = 4(x + 2) and…

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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: 5. The area bounded by the curve y = 3x – x3 and the line y = 2 is revolved about the line y = 2.…

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Q: Use cylinder shell method to graph and find volume: y=sqrt(x), y=0, x=1, about x=-1

A: If a region is bounded by a curve y=fx and x-axis on the interval a,b and it is rotating about a…

Q: The area bounded by the parabola x² – 2x + y = 3, in the - second quadrant about the line y = 4.…

A: Area and volume

Q: 9. The area bounded by the parabola x 4y and the line x = 4 - 2y is revolved about the line y 4.…

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Q: Find the volume of the solid generated by revolving the region about the given line. 20) The region…

A: To find the volume obtained by rotating the region in second quadrant bounded between y = 4 – x2 and…

Q: Find the volume of the solid generated by revolving the region about the given line. The region in…

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Q: (b) Use differentials to estimate the maximum error in the calculated volume. What is the relative…

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Q: 3.Find the volume of the solid formed by revolving the region bounded by the graph of f(x) = vsin x…

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Q: The area bounded by the curve y=(x^2-2)^2 and the x-axis is revolved about the y-axis. Find the…

A: the volume revolved about x-axis given by the curve f(x) and limits a to b is  volume = π∫ab(fx]2dx

Q: Determine the volume generated when the area bounded by the curves y-sinx and y%3cosx from x-0 to…

A: Aim: We need to find the volume of the solid obtained by revolving the bounded region (light yellow)…

Q: y = 3x - x² and y = 2x

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Q: The edge of a cube was found to be 15 cm with a possible error in measurement of 0.2 cm. Use…

A: The given data is: Edge of the cube x=15 cmPossible error dx=0.2 cm

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: The area bounded by the curve y 2 - 4x and the line 2x -y 12 is revolved about the y-axis. Find the…

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Q: Find the volume of the solid generated by revolving the region about the given line. 14) The region…

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Q: The region bounded by the curve: y = e * and y=0 for x20is rotated about the x – axis. Calculate its…

A: By using volume of solid formula, we calculate the required volume.

Q: A thin 5 cm wire represented by 0 < x < 5 has density function p(x) = 9/cm. Find the mass of the…

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Q: 2. Determine the approximate volume of a cube whose edge is 19.95 cm, using differential. 3. Use…

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Q: find volume of area bounded by y = x 2x +3 and y = 3 about line y = 3 an |the

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Q: Find the volume generated by revolving bout the line x = -1 the area bounded by (y + 2)° = 4(x + 2)…

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Q: Find the volume of the cone generated by revolving about the y-axis the area bounded by the line 2x…

A: We have given the curves; 2x+y=2 and y=2x+x2-x3 Which generates the cone revolving about the y-axis.

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.