Find the volume of the solid generated by revolving the curve y² – x1l – x² = 64 between x = 0 and x =2 about the х — ахіs. -

Q: Find the differential euqation representing the family of cicles of radius unity and center anywhere…

A: The order of the  differential equation of a given relation is the number of arbitrary constants in…

Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

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Q: Find the area of the surface swept out by revolving the para- metric curve x = 5 cost + 5t sin t y =…

A: Area under curve.

Q: 1 — х

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Q: Find a parametrization of the curve ²/3 + y²/3 = 1 and use it to compute the area of the interior.

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Q: Find the area of the part of the hyperbolic araboloid z = y² – x² nat lies between the cylinders x²…

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Q: Compute the surface area of the surface generated by revolving the curve c(t) = (t, e') about the…

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Q: 1. What is the differential for the total surface area of a frustum of a cone with l as the slant…

A: Given slant height l. Let r and R be the radii of the frustum. Let h be the height of the frustum.…

Q: y = h(xlb)2.

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Q: Use differentials to estimate the change in f (x, y, z) = x² In(5yz + 1) as (x, y, z) changes from…

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Q: Find the center of the mass of a thin plate of constant density & covering the region bounded by the…

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Q: 3. Let C be the part of the circle with radius 3 in the first quadrant as in the picture. 3. (a)…

A: To solve the following paramteric equation problem

Q: The longest interval in which the 1.V.P y" +(tanx)y- xy = x, y(1) = 3, y'(1) =0 surlay has a…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 15x from (15, 15) to (0,0). NOTE:…

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Q: take the fequan bunded by Hhe Seguen Curve fla).2+ Sinlx) the x atis 3R and X= Vz X:0 and fond the…

A: We will find out the required value.

Q: Find the area of rotating face farmeal by rotading given by thepart 아 the curve y =Inx, 1<x42 around…

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Q: )Find the volume of the solid obtained by rotating the sine function between x 0 and x t about the…

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Q: (iii) The moment of inertia I of an annulus of inner radius 'a' outer radius 'b' and mass 'm' is…

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Q: If v is the velocity field of a fluid, the flux of v across C is equal to the flow rate ( amount of…

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Q: Q₁) Find $dz 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using…

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Q: 5. A heavy rock blown straight up from the ground by a dynamite blast. The velocity time t during…

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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.