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Title: Complex Integration on Real Intervals
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Series: Complex Analysis
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YouTube-Title: Complex Analysis 17 | Complex Integration on Real Intervals
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Bright video: https://youtu.be/tJf1Vpl3_88
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Dark video: https://youtu.be/i2pkG8CV9NI
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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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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: ca17_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: Let $\gamma: [0,1] \rightarrow \mathbb{C}$ be a continuous map. Which statement is not correct?
A1: $ \int_0^1 \gamma(t) dt $ is well-defined.
A2: $ \int_0^1 \gamma(t) dt $ is a complex number.
A3: $ \int_0^1 \gamma(t) dt $ is an antiderivative of $\gamma$.
A4: $ \int_0^1 \gamma(t) dt $ has a real and an imaginary part.
Q2: Let $\gamma: [0,1] \rightarrow \mathbb{C}$ be given by $\gamma(t) = 2t + i 4 t^3$. What is $ \int_0^1 \gamma(t) dt $?
A1: $1$
A2: $1 + i$
A3: $2$
A4: $2 + 4 i$
Q3: Which number is larger than $$ \left| \int_0^1 \exp(\pi i t) dt \right| $$
A1: $1$
A2: $\frac{1}{2}$
A3: $\frac{1}{\pi}$
A4: $0$
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Last update: 2024-10
