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Title: Second Fundamental Theorem of Calculus
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Series: Real Analysis
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Chapter: Riemann Integral
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YouTube-Title: Real Analysis 55 | Second Fundamental Theorem of Calculus
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Bright video: https://youtu.be/SJC4DGuyg4c
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Dark video: https://youtu.be/ZS5DatwHksQ
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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: ra55_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 $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function and $F: \mathbb{R} \rightarrow \mathbb{R}$ be an antiderivative of $f$. Is $G = F+2$ also an antiderivative?
A1: Yes!
A2: No, never!
A3: No, not necessarily.
Q2: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function and $F,G: \mathbb{R} \rightarrow \mathbb{R}$ be two antiderivatives of $f$. What is $F-G$?
A1: $\sin(x)$
A2: a constant
A3: $x$
A4: In general, it could be anything.
Q3: What is the integral $\int_0^x \cos(t) , dt$?
A1: $0$
A2: $\cos(x)$
A3: $\cos(\exp(x))$
A4: $\sin(x) $
A5: $\cos(\sin(x))$
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Last update: 2025-01
