What is the area, br^2, of the surface of the revolution obtained by rotating the graph of the function x =y between the y = 0, y= 3 abscissa points about the y-axis? 97 O A) 87 O B) OC) OD) OE) 38

Q: a mathematician designs a patio for her backyard to follow a particular curve.  a region of the…

A: Solution is given below:

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Q: enclosed betw parabola y = x2

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Q: y = } + sxs1 <x<1 2

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Q: find the area of the surface obtained by rotating the curve along the x-axis

A: Surface area along x-axis

Q: nd the area of the surface generated by revolving the curve x= Osys2, about the y-axis. 3

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Q: B) Find the area of the region enclosed by the Parabola y = 2 – x2 and the line y + x = 0 ?

A: The region is bounded by y=2-x2 and y+x=0

Q: +³ 3 y=a+t, √a ≤ t ≤ √a X || +at,

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Q: Find the surface area generated by revolving one arc (first quadrant) of y = cos x about the x-axis.…

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Q: Find the exact area of the surface obtaimed by the curre around the x-axis J relating the g= re √6-x…

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Q: Use rectangles to estimate the area under the parabola y = x2  from 0 to 1

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Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3

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.