3. 10 8- y=5 6- 4- 2- y=9-x -4-3 -2 -1 1 2 3 The diagram shows the curve y = 9 – x² and the line y = 5. Find the shaded area.

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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### Problem 3:

The following diagram illustrates two mathematical functions: \( y = 9 - x^2 \) and \( y = 5 \).

The graph presented comprises:
- A parabolic curve represented by the equation \( y = 9 - x^2 \).
- A horizontal line represented by the equation \( y = 5 \).

**Axes:**
- The horizontal axis (x-axis) ranges from -4 to 4.
- The vertical axis (y-axis) ranges from 0 to 10.

**Intersections:**
- The parabola \( y = 9 - x^2 \) intersects with the y-axis at \( (0, 9) \) and opens downwards.
- The horizontal line \( y = 5 \) intersects the y-axis at \( (0, 5) \).

**Objective:**
Find the shaded area enclosed by the curve \( y = 9 - x^2 \) and the line \( y = 5 \).

This involves calculating the definite integral between the points where the parabola intersects the line \( y = 5 \). These points of intersection can be determined by solving the equation \( 9 - x^2 = 5 \).
Transcribed Image Text:### Problem 3: The following diagram illustrates two mathematical functions: \( y = 9 - x^2 \) and \( y = 5 \). The graph presented comprises: - A parabolic curve represented by the equation \( y = 9 - x^2 \). - A horizontal line represented by the equation \( y = 5 \). **Axes:** - The horizontal axis (x-axis) ranges from -4 to 4. - The vertical axis (y-axis) ranges from 0 to 10. **Intersections:** - The parabola \( y = 9 - x^2 \) intersects with the y-axis at \( (0, 9) \) and opens downwards. - The horizontal line \( y = 5 \) intersects the y-axis at \( (0, 5) \). **Objective:** Find the shaded area enclosed by the curve \( y = 9 - x^2 \) and the line \( y = 5 \). This involves calculating the definite integral between the points where the parabola intersects the line \( y = 5 \). These points of intersection can be determined by solving the equation \( 9 - x^2 = 5 \).
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