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Title: Comparison Test for Integrals
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Series: Real Analysis
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Chapter: Riemann Integral
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YouTube-Title: Real Analysis 61 | Comparison Test for Integrals
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Bright video: https://youtu.be/yEp9BTDgOjk
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Dark video: https://youtu.be/WoiYPegVj6M
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Ad-free video: Watch Vimeo video
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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: ra61_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $f,g: [0,\infty) \rightarrow [0,\infty)$ be functions such that the restrictions to compact intervals are Riemann-integrable. Which claim is correct?
A1: If $\int_0^{\infty} g(x) dx$ converges, then $\int_0^{\infty} f(x) dx$ converges.
A2: If $\int_0^{\infty} g(x) dx$ converges and $f \leq g$, then $\int_0^{\infty} f(x) dx$ converges.
A3: If $\int_0^{\infty} g(x) dx$ converges and $g \leq f$, then $\int_0^{\infty} f(x) dx$ converges.
A4: If $\int_0^{\infty} g(x) dx$ diverges and $g \leq f$, then $\int_0^{\infty} f(x) dx$ converges.
Q2: Let $f,g: [0,\infty) \rightarrow [0,\infty)$ be functions such that the restrictions to compact intervals are Riemann-integrable. Which claim is correct?
A1: If $\int_0^{\infty} g(x) dx$ diverges, then $\int_0^{\infty} f(x) dx$ diverges.
A2: If $\int_0^{\infty} g(x) dx$ diverges and $f \leq g$, then $\int_0^{\infty} f(x) dx$ diverges.
A3: If $\int_0^{\infty} g(x) dx$ diverges and $g \leq f$, then $\int_0^{\infty} f(x) dx$ diverges.
A4: If $\int_0^{\infty} g(x) dx$ diverges and $g \leq f$, then $\int_0^{\infty} f(x) dx$ converges.
Q3: Is the integral $\int_1^{\infty} \frac{1-x}{x^2} dx$ convergent?
A1: Yes!
A2: No!
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Last update: 2025-01
