HW: Find the area of the surfoce generaled by revolving 1. x= Vy,1sy s8 about the x- axis.

Q: the Area under tro choid one arch of the ( = 70-1sine. 1Sine, y= 1cose

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Q: Find the larger area formed by x² + 3y² + 7x = 3 and 2x² – 6y = 5.

A: Integration of function expression under certain limits give the value of area between function…

Q: Sketch the curves y = 3x and y = x and determine the area enclosed by them.

A: we can find the area enclosed by the curve by setting up the double integral. to find the limit of…

Q: Find the area of the curve: y = 9-x² and the x-axis

A: We are authorized to answer one question at a time, so we are answering the first one. Please repost…

Q: +³ 3 y=a+t, √a ≤ t ≤ √a X || +at,

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Q: Find the area between the two curves y = 3 y = x² – 1 1+ x2'

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Q: Find the surface area of the object obtained by rotating x = Vy-6 2sys3 about the y-axis.

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Q: Find the y²=x,x²-2x +3y=2 area between the two curves..

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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.