-
Title: Properties of the Riemann Integral for Step Functions
-
Series: Real Analysis
-
Chapter: Riemann Integral
-
YouTube-Title: Real Analysis 50 | Properties of the Riemann Integral for Step Functions
-
Bright video: https://youtu.be/6Pb97_7huwI
-
Dark video: https://youtu.be/NIc9uF7cst0
-
Ad-free video: Watch Vimeo video
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Exercise Download PDF sheets
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: ra50_sub_eng.srt missing
-
Timestamps (n/a)
-
Subtitle in English (n/a)
-
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: $\int_0^2 \psi(x) dx \geq \int_0^2 \phi(x) dx$
-
Last update: 2025-01
