Find the center of the mass of a thin plate of constant density & covering the 3 region bounded by the x-axis and the curve y=7 cos x, , -3 sxs3. 2

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: Calculate exactly the volume of the solid obtained by rotating the area delimited by y=(x-2)^2 and…

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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 a center of mass of a thin plate of density 8 = 3 bounded by the lines y = x and x = 0 and the…

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Q: Given the area bounded by the curve y^2 = 4x and y^2 = 8x − 8. Determine the centroid area bounded…

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Q: A certain liquid of sp.gr. = 0.80flows through a 150-mm-diameter pipe under a pressure of 103.5 kPa.…

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Q: Find the vol. of the solid generated by revolving the region bounded by the graphs of the eq. about…

A: Given: Solid generated by revolving the region bounded by graphs of the equation about the line y=4…

Q: Find a center of mass of a thin plate of density 8 = 5 bounded by the lines y = x and x = 0 and the…

A: Center of mass of the plate is given by  x,y=MyM,MxM here M=∫∫D δx,ydAMx=∫∫D yδx,ydAMy=∫∫D xδx,ydA…

Q: The region bounded by the curve y=x²-2 and the lines y=-2 and x=2 is rotated about the line y=-2.…

A: The two curves are y=x2-2  &  y=-2 & x=-2

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.