DO NOT ANSWER IN DECIMAL FORM ANSWER SIMILIAR IN the manner I attempted to do ### Calculating the Area Enclosed by Given CurvesIn this lesson, we will learn how to find the area enclosed by two curves, specifically focusing on the following curves:\[ y = 3 \sin \left( \frac{\pi x}{7} \right), \quad y = \frac{6}{7} x \]### Graphical Approach to Finding the Enclosed Area#### Steps to solve the problem:1. **Graph the Functions:** - Plot the curves given by the equations $ y = 3 \sin \left( \frac{\pi x}{7} \right) $ and $ y = \frac{6}{7} x $ on the same coordinate axes. 2. **Identify the Region to Integrate:** - Identify the region enclosed by the two curves. This region will be shaded on the graph.3. **Choose the Axis of Integration:** - Decide whether to integrate with respect to $ x $ or $ y $. This decision is based on which method simplifies the calculation. 4. **Draw an Approximating Rectangle:** - Draw a typical approximating rectangle to visualize the process of integration.#### Graphs and Explanations:- **Top Left Graph:** - The graph plots the curves $ y = 3 \sin \left( \frac{\pi x}{7} \right) $ and $ y = \frac{6}{7} x $ with the shaded region indicating the enclosed area. - A vertical red rectangle (typical approximating rectangle) is drawn in the first quadrant within the enclosed region. This rectangle represents a small segment used for integration. - **Top Right Graph:** - Similar to the top left graph but with a different placement of the typical approximating rectangle, shown in the fourth quadrant.- **Bottom Left Graph:** - This graph shows the curves with the enclosed area shaded. The red rectangle is drawn horizontally, showing an integration approach with respect to $ y $.- **Bottom Right Graph:** - The correct integration approach is depicted with the red rectangle in the first quadrant, fitting between the two curves.### Correct Solution Identification:- The correct graph for solving this problem is the **bottom right graph**. It depicts the integration with respect to $ y $, as denoted by the green check mark.### Finding the Area:Finally, calculate

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Description: DO NOT ANSWER IN DECIMAL FORM ANSWER SIMILIAR IN the manner I attempted to do ### Calculating the Area Enclosed by Given CurvesIn this lesson, we will learn how to find the area enclosed by two curves, specifically focusing on the following curves:\[

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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y-3 sin(프), y-흑x y y -2 2 -2 -2 -6 -6 y y 2 3 -1 3 -3 -4 -5 Find the area of the region. 21 – 5.25 2. 2. 2. 2. 2.

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y-3 sin(프), y-흑x y y -2 2 -2 -2 -6 -6 y y 2 3 -1 3 -3 -4 -5 Find the area of the region. 21 – 5.25 2. 2. 2. 2. 2.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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DO NOT ANSWER IN DECIMAL FORM ANSWER SIMILIAR IN the manner I attempted to do

### Calculating the Area Enclosed by Given Curves

In this lesson, we will learn how to find the area enclosed by two curves, specifically focusing on the following curves:
\[ y = 3 \sin \left( \frac{\pi x}{7} \right), \quad y = \frac{6}{7} x \]

### Graphical Approach to Finding the Enclosed Area

#### Steps to solve the problem:

1. **Graph the Functions:**
- Plot the curves given by the equations $ y = 3 \sin \left( \frac{\pi x}{7} \right) $ and $ y = \frac{6}{7} x $ on the same coordinate axes.

2. **Identify the Region to Integrate:**
- Identify the region enclosed by the two curves. This region will be shaded on the graph.

3. **Choose the Axis of Integration:**
- Decide whether to integrate with respect to $ x $ or $ y $. This decision is based on which method simplifies the calculation.

4. **Draw an Approximating Rectangle:**
- Draw a typical approximating rectangle to visualize the process of integration.

#### Graphs and Explanations:

- **Top Left Graph:**
- The graph plots the curves $ y = 3 \sin \left( \frac{\pi x}{7} \right) $ and $ y = \frac{6}{7} x $ with the shaded region indicating the enclosed area.
- A vertical red rectangle (typical approximating rectangle) is drawn in the first quadrant within the enclosed region. This rectangle represents a small segment used for integration.

- **Top Right Graph:**
- Similar to the top left graph but with a different placement of the typical approximating rectangle, shown in the fourth quadrant.

- **Bottom Left Graph:**
- This graph shows the curves with the enclosed area shaded. The red rectangle is drawn horizontally, showing an integration approach with respect to $ y $.

- **Bottom Right Graph:**
- The correct integration approach is depicted with the red rectangle in the first quadrant, fitting between the two curves.

### Correct Solution Identification:

- The correct graph for solving this problem is the **bottom right graph**. It depicts the integration with respect to $ y $, as denoted by the green check mark.

### Finding the Area:

Finally, calculate

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