The task is to sketch the region enclosed by the given curves and find its area. The curves are defined by the equations:1. $ y = 3 \cos(5x) $2. $ y = 3 - 3 \cos(5x) $The range for $ x $ is $ 0 \leq x \leq \frac{\pi}{5} $.### Graph Descriptions:**Graph 1 (Top Left):**- The graph shows two curves, $ y = 3 \cos(5x) $ and $ y = 3 - 3 \cos(5x) $, intersecting over the given range for $ x $.- The curves form a symmetric shape, with the region between them shaded in blue.- This region is enclosed above by the $ y = 3 - 3 \cos(5x) $ and below by $ y = 3 \cos(5x) $.**Graph 2 (Top Right):**- Similar to the first graph, this also depicts the curves $ y = 3 \cos(5x) $ and $ y = 3 - 3 \cos(5x) $, intersecting.- The region between the two curves is shaded blue, illustrating the enclosed area.**Graph 3 (Bottom Left):**- Presents the same functions flipped about the y-axis.- Again, the enclosed area is shown in blue, with curves forming a shape symmetric to the top graphs.**Graph 4 (Bottom Right):**- Displays the same curves as the previous graphs.- The enclosed area between the curves is shaded in blue, mirroring the enclosed shape seen in other graphs.Each diagram illustrates the same enclosed section between the two curves over the specified domain.### Task:Calculate and find the area of the blue-shaded region enclosed by these curves over the interval $ 0 \leq x \leq \frac{\pi}{5} $.

Answered: Image /qna-images/answer/1b138fb8-23e4-4ade-b0f5-fbc281e96e5f.jpg

Sketch the region enclosed by the given curves. y = 3 cos(5x), y= 3 – 3 cos(5x), 0 < x< 1/5 y y 6- 2 4 0.2 8.3 0.4 0.5 0.6 2 0.1 0.2 0.3 0.4 0.5 0.6 -2 -6F y y 6- 2 4 0.1 0.3 0.4 0.5 06 0.1 0.2 0.3 0.4 0.5 0.6 -2 -4 O-6H Find its area.

Sketch the region enclosed by the given curves. y = 3 cos(5x), y= 3 – 3 cos(5x), 0 < x< 1/5 y y 6- 2 4 0.2 8.3 0.4 0.5 0.6 2 0.1 0.2 0.3 0.4 0.5 0.6 -2 -6F y y 6- 2 4 0.1 0.3 0.4 0.5 06 0.1 0.2 0.3 0.4 0.5 0.6 -2 -4 O-6H Find its area.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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.

Question

The task is to sketch the region enclosed by the given curves and find its area. The curves are defined by the equations:

1. $ y = 3 \cos(5x) $
2. $ y = 3 - 3 \cos(5x) $

The range for $ x $ is $ 0 \leq x \leq \frac{\pi}{5} $.

### Graph Descriptions:

**Graph 1 (Top Left):**

- The graph shows two curves, $ y = 3 \cos(5x) $ and $ y = 3 - 3 \cos(5x) $, intersecting over the given range for $ x $.
- The curves form a symmetric shape, with the region between them shaded in blue.
- This region is enclosed above by the $ y = 3 - 3 \cos(5x) $ and below by $ y = 3 \cos(5x) $.

**Graph 2 (Top Right):**

- Similar to the first graph, this also depicts the curves $ y = 3 \cos(5x) $ and $ y = 3 - 3 \cos(5x) $, intersecting.
- The region between the two curves is shaded blue, illustrating the enclosed area.

**Graph 3 (Bottom Left):**

- Presents the same functions flipped about the y-axis.
- Again, the enclosed area is shown in blue, with curves forming a shape symmetric to the top graphs.

**Graph 4 (Bottom Right):**

- Displays the same curves as the previous graphs.
- The enclosed area between the curves is shaded in blue, mirroring the enclosed shape seen in other graphs.

Each diagram illustrates the same enclosed section between the two curves over the specified domain.

### Task:

Calculate and find the area of the blue-shaded region enclosed by these curves over the interval $ 0 \leq x \leq \frac{\pi}{5} $.

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