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: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

A:

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

A: Introduction: The area of the region enclosed by the curves y=f(x) and y=g(x) between a≤x≤b is given…

Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: Sketch the region enclosed by the given curves. y = 4 cos(x), y = 4 - 4 cos(x), 0 s xs n y y 4 2 1.0…

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Q: Find the area of one the graphs of bounded by cos Xe region Sinx and

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Q: Sketch the region enclosed by the given curves. y 2 cos(7x), y = 2 sin(14x), X = 0, 14 y 2.0+ 1.5…

A: We have to find the area between the curves.

Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. a = 4 b = 2…

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Q: Sketch the region enclosed by the given curves. y = 3 cos(9x), y = 3 – 3 cos(9x), OSxS1/9

A: Solution is in step 2

Q: A region in the (z, y)-plane is bounded by the curves y = 2 cos z and y=-+ for -/2<zS=/2. These…

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Q: Sketch the region enclosed by the given curves. y = 5 cos(3x), y = 5 sin(6x), х%3D 0, x = T/6 y y 5t…

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Q: 19. Between y = e¯* and y = 4(x - x²). |

A: 19)  First plot the graph for the given curves  Then find the intersection point Now find the area…

Q: To identify how much heat is required to bring a kettle of water to its boiling point, you are…

A: Here,

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: To find the volume of the solid obtained by rotating the region bounded by y=7sinx, and…

Q: Find the area of the region described. 2 The region in the first quadrant bounded by y=x' and y = 2

A:

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.