1. The graph of a function f(r) is shown below. Answer the following questions using geometry. y = f(x) a) 3f(r) dr b) %3D rp (r)f c) (r)| dr + 2f(r) dr =

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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### Introduction

1. The graph of a function \( f(x) \) is shown below. Answer the following questions using geometry.

#### Diagram Explanation

- The graph is a piecewise linear function.
- The \( x \)-axis ranges from 0 to 6.
- The \( y \)-axis ranges from -3 to 3.

#### Graph Details

1. The graph starts at the point (0, 3) and follows a straight line.
2. It moves downward to the point (2, 0).
3. It continues to the point (4, -3).
4. Then, the graph ascends to the point (6, 0).

### Questions

a) Evaluate \( \int_{0}^{3} 3f(x) \, dx \).

b) Evaluate \( \int_{1}^{4} f(x) \, dx \).

c) Evaluate \( \int_{4}^{3} |f(x)| \, dx + \int_{3}^{6} 2f(x) \, dx \).
Transcribed Image Text:### Introduction 1. The graph of a function \( f(x) \) is shown below. Answer the following questions using geometry. #### Diagram Explanation - The graph is a piecewise linear function. - The \( x \)-axis ranges from 0 to 6. - The \( y \)-axis ranges from -3 to 3. #### Graph Details 1. The graph starts at the point (0, 3) and follows a straight line. 2. It moves downward to the point (2, 0). 3. It continues to the point (4, -3). 4. Then, the graph ascends to the point (6, 0). ### Questions a) Evaluate \( \int_{0}^{3} 3f(x) \, dx \). b) Evaluate \( \int_{1}^{4} f(x) \, dx \). c) Evaluate \( \int_{4}^{3} |f(x)| \, dx + \int_{3}^{6} 2f(x) \, dx \).
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