3 2 -1 -2 -3 The graph above shows the base of an object. Compute the exact value (in terms of T) of the volume of the object, given that cross sections (perpendicular to the base) are semi-circles, with their diameters on the base. V =

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Q: The graph above shows the base of an object. Conpute the exact value ( in terms of pi) of the volume…

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Q: 2. x = 4y – y² and x = 4 – y |

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Q: y = f(x) 2r cross-section y = g(x) base view The base of a certain solid is an equilateral triangle…

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Q: y = f(x) 2r 2r cross-section y = g(x) base view The base of a certain solid is an equilateral…

A: Solution:-

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Q: x + y = 7, x = 0, and y = 0 Use the disk method to find the volume (in units3) when the region is…

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Q: a. Find the vertex and opening of the parabola b. Find the points of intersection of the given…

A: 2. Given : curves are  x = 4y − y2 and  x = 4 − yTo find:a. Find the vertex and opening of the…

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A: Rewrite the equation y=5-12x, to find f(y) and identify the limits of y. y=5-12x12x=5-yx=25-y=10-2y…

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Q: y = f(x) 2r 2r cross-section y = g(x) base view The base of a certain solid is an equilateral…

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4 -4 The graph above shows the base of an object. Compute the exact value (in terms of T) of the…

A: Use the slice method in which take a cross-section area and integrate for whole region.

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Q: 1 2 -1 -2 6 V = 8 The graph above shows the base of an object. Compute the exact value of the volume…

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Q: A solid lies between planes perpendicular to the x-axis at x = -6 and x = 6. The cross-sections…

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Q: A solid ballis exactly fitted inside the cubical box of side a.The volume of the ball is 4/3 pi a3

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A: Topic:- application of integration

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Q: The plane region is revolved completely about the y-axis to sweep out a solid of revolution.…

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Q: 4- 2 2 -5 The graph above shows the base of an object. Compute the exact value of the volume of the…

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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.