What is the volume of the body of rotation formed by rotating the region bounded by the function y = 3 - x ^ 2 and the ox - axis around the line y = 3?

Q: Find the surface area of the solid generated by rotating the curve x = 1/3 y^(3/2) - y^(1/2), 0 <= y…

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

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Q: Find the volume of the figured form by rotation f(x) = 1 + 2x^2 around the line y = 5 on the…

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Q: 3. A $12,300 investment earns 4.75%/a in interest, compounded quarterly. a) Determine the value of…

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Q: A rectangular shaped region is changing with time and increasing in the x direction at the rate of 2…

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Q: Find the centroid of the region bounded by y = 9 − x^2 and y = 0

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Q: Find the centroid of the region in the plane enclosed by the curves y = +-(1 - x2)^(-1/2) and the…

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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: Let S be the passage of R ^ 2 defined by the parabola with equation y = 18-x ^ 2 and by the line…

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Q: Find the area of the plane region that lies below the line y = 2x and between the parabolas y= 2x^2…

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Q: Find the surface area generated by rotating x=4*sqrt(t), y= ((t^3)/3)+(1/2t^2), 1<=t<=3 around the…

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Q: The area R in the plane is bounded by the curves given by (x = y^2 + 2), (y = x - 4) and (y = 0), as…

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Q: find the lateral (side) surface area of the cone generated by revolving the line segment y=7/3x, 0…

A: What is Solid of Revolution: A solid can be formed by revolving a region in two dimensional…

Q: find the volume of the revolution of the area bounded by y=4x-x^2 and y=3 rotated about the y axis.

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Q: Locate the centroid of the volume bounded by the equation y^2 = 4x, x = 1 and the x-axis and…

A: The solid is symmetric figure , the centroid lies on the x axis. The y and z coordinates are 0.

Q: Determine the ordinate of the centroid of the area bounded by the curve x^2 =8y and the line 2x-y=0

A: Given curves are x2=8y and 2x−y=0. We have to find the ordinate of the centroid of the area bounded…

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.