Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 9 sin(x), y = 9 cos(x), Osxs about y = -1 Sketch the region. 6 2 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 ...... ...... -0.4 -0.2 -0.4 -0.2 -04 -0.2 0.2 0.4 0.6 0.8 1.0 -0.4 -0.2 0.2 0.4 0.6 0.8 1.0 . ... ... . ....... ....... ... ... - Sketch the solid and a typical disk or washer. AInteractive 30 Graph OHelp 15 10 -1 -0.5 10 ~15 Interactive 3D Graph OHelp Interactive 3D Graph OHelp AInteractive 3D Graph O Help 15 15 15 10 10- 10- 5 5 5 H|||||||H ++++||+|H||||||| -x -1 -0.5 -1 -0.5 0.5 -1 -0.5 10 -10 10 r-15 15 15 r-15

Q: d the work done by F= 1, and the curve yax The amount of work done is Type a simplified fraction) in…

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Q: ch the region enclosed by the given curves. y - cos(x), y- sin(2x), 0sxs 2. -1 -1 -라

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A: Since you posted the multiple question. I am answering the first one. Please post the question for…

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A: Given: dydt=-2(y-4)y4(y-1) To draw: phase line.

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Q: Find the area of the shaded region. -1.0 -0.5 y 8 6 y=3e* 4 2 0.5 (1, 3e) y=3xe¹² 1.0 1.5 2.0 X

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Q: ○cV=[(12-)-(12-y) |か

A: Given that: The equation of the curves are y = x and y = x2 , about line x = 12.

Q: Question 10 Let f(x)=√3x-2 on the interval volume of the resulting solid. 43x 135 83m 125 83x 135…

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Q: A 3 2 1 0 -1 -2 -3 R 5 -4 -3 -2 y S -1 0 1 2 3 Part A: Find the area of R + S. 4 5 2

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Q: Surface area of Revolution 1. Find the area of the surface obtained by rotating the curve y? = 4x +…

A: Since you post more than one non interlinking questions, so as per our guideline we can solve only…

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Q: (a) Recall that dA gives us the area of a region R in the xy-plane. Find the area of the region R =…

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Q: Let S be the statement: The reciprocal of any irrational number is irrational. (The reciprocal of a…

A: We are given a statement S. S : The reciprocal of any irrational number is irrational .

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A: To find the volume of the given shaded region rotated about the y-axis. First find the value of m…

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A: Given that ,Find the area A of the region enclosed by the cardioid and the slope m of the tangent…

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.