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Title: Properties of the Riemann Integral for Step Functions
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Series: Real Analysis
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Chapter: Riemann Integral
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YouTube-Title: Real Analysis 50 | Properties of the Riemann Integral for Step Functions
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Bright video: https://youtu.be/6Pb97_7huwI
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Dark video: https://youtu.be/NIc9uF7cst0
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Ad-free video: Watch Vimeo video
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Exercise Download PDF sheets
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: ra50_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Which is not a property of the map $\phi \mapsto \int_a^b \phi(x) dx$?
A1: linear
A2: monotonic
A3: additive
A4: injective
A5: homogeneous
Q2: Let $\phi : [0,2] \rightarrow \mathbb{R}$ and $\psi : [0,2] \rightarrow \mathbb{R}$ be two step functions with $\phi(x) \leq \psi(x)$ for all $x \in [0,2]$. Which of the following statements is definitely false?
A1: $\int_0^2 \psi(x) dx = \int_0^2 \phi(x) dx$
A2: $\int_0^2 \psi(x) dx < \int_0^2 \phi(x) dx$
A3: $\int_0^2 \psi(x) dx > \int_0^2 \phi(x) dx$
A4: $\int_0^2 \psi(x) dx \leq \int_0^2 \phi(x) dx$
A5: $\int_0^2 \psi(x) dx \geq \int_0^2 \phi(x) dx$
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Last update: 2025-01
