In the definition of the area under the curve y = f(x) on [a, b], the function f is required to be and nonnegative on [a, b].
In the definition of the area under the curve y = f(x) on [a, b], the function f is required to be and nonnegative on [a, b].
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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![**Question:**
Riemann sums give better ________________ for larger values of *n*.
**Answer:**
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Riemann sums give better ________________ for larger values of *n*.
**Answer:**
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![### Understanding the Area Under the Curve
In the definition of the area under the curve \( y = f(x) \) on the interval \([a, b]\), the function \( f \) is required to be ________________ and nonnegative on \([a, b]\).
[Insert user input box here]
#### Explanation:
For calculating the area under a curve, it is essential that the function \( f(x) \) is ________________ (e.g., continuous, integrable). Additionally, \( f(x) \) must be nonnegative over the interval \([a, b]\), meaning \( f(x) \geq 0 \) for all \( x \) in \([a, b]\).
In this context, ensuring that the function meets these criteria guarantees that the calculated area is accurate and meaningful.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11c3e735-47a2-4be2-bcf0-76944b0744ea%2F876bd494-c8f0-4583-b009-be24097a656d%2F71z80hq_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Area Under the Curve
In the definition of the area under the curve \( y = f(x) \) on the interval \([a, b]\), the function \( f \) is required to be ________________ and nonnegative on \([a, b]\).
[Insert user input box here]
#### Explanation:
For calculating the area under a curve, it is essential that the function \( f(x) \) is ________________ (e.g., continuous, integrable). Additionally, \( f(x) \) must be nonnegative over the interval \([a, b]\), meaning \( f(x) \geq 0 \) for all \( x \) in \([a, b]\).
In this context, ensuring that the function meets these criteria guarantees that the calculated area is accurate and meaningful.
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