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Title: Integrals on Unbounded Domains
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Series: Real Analysis
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Chapter: Riemann Integral
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YouTube-Title: Real Analysis 60 | Integrals on Unbounded Domains
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Bright video: Watch on YouTube
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Dark video: Watch on YouTube
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Ad-free video: Watch Vimeo video
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Original video for YT-Members (bright): Watch on YouTube
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Original video for YT-Members (dark): Watch on YouTube
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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: ra60_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: Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ given by $f(x) = x^2$. Which claim is not correct?
A1: $f|_{[a,b]}$ is Riemann-integrable for all $a \leq b$.
A2: $\int_a^b f(x) , dx $ is well-defined for all $a \leq b$.
A3: $ \int_0^\infty f(x) , dx$ converges.
Q2: What is the integral $ \int_{-\infty}^{0} \exp(x) , dx$
A1: $-1$
A2: $1$
A3: $-\pi$
A4: $\pi$
A5: $\frac{1}{2}$
A6: $-\frac{1}{2}$
Q3: What is the limit $$ \lim_{c \rightarrow \infty} \int_{-c}^{c} x , dx$$
A1: Not defined!
A2: $\infty$
A3: $-\infty$
A4: $0$
Q4: Does the improper Riemann integral $$ \int_{-\infty}^{\infty} x , dx$$ exist?
A1: No!
A2: Yes!
A3: The notation $\int_{-\infty}^{\infty}$ never makes sense.
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Last update: 2025-01