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Q: Draw the area bounded by function y = x^2 + 1 and line y = 5, then calculate the volume of the solid…

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Q: Given an area D bounded by curve y = 4x−x^2, line x+y = 6, and y-axis. Find the volume if the area D…

A: We are given an area D bounded by curve y = 4x - x2, line x + y = 6, and y-axis. We need to find the…

Q: Find the center of mass of a thin plate of constant density covering the given region. The region…

A: We have to solve the given problem.

Q: Find the volume of a solid whose base is the unit circle x^2 + y^2 = 1 and the cross sections…

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Q: Find the volume of the region bounded by y=x^2 Below the x axis And on the right by the line x=3…

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Q: Find the volume of the solid formed by revolving the region bounded by the graphs y = √x and y = x^2…

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Q: Revolve the region bound by y=x2+1,y=1-x and x=1 around by x-axis.

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Given curves are  4x-y=0⇒y=4xy=x2

Q: A body T with the parameters  (1/2)(sqrt(x^2)+(y^2))≤z≤sqrt(16-(x^2)-(y^2) Use the sphere…

A: The given problem is to find the volume of the body formed by the cone and spherical region, we have…

Q: = 4, where cross- Find the volume of a solid whose base is the circle x² + y² sections perpendicular…

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Q: ind the volume

A: To find the volume of the solid that is obtained by rotating the curve y=ex/2+e−x/2 about the x-axis…

Q: Find the Volume of the 2 genrated by revolving the region in the first quadrent that is above the…

A: we'll use the method of cylindrical shells. This method involves integrating the volume of each…

Q: Find the volume generated revolved about when the area of the curve the line y=-4 x² = -y is

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Q: enclosed

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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.