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Title: First 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 54 | First Fundamental Theorem of Calculus
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Bright video: https://youtu.be/AKhlP6IHDLk
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Dark video: https://youtu.be/wEd0hk-ejp4
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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: ra54_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 $F$ differentiable?
A1: Yes!
A2: No, never!
A3: No, not necessarily.
Q2: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $f(x) = \cos(x)$. Which one the following functions is not an antiderivative of $f$?
A1: $F(x) = \sin(x) + 55$
A2: $F(x) = \sin(x)$
A3: $F(x) = \sin(x) - \pi $
A4: $F(x) = 2 \sin(x)$
Q3: What is derivative of the function $x \mapsto \int_0^x \cos(\exp(t)) , dt$
A1: $0$
A2: $\cos(x)$
A3: $\cos(\exp(x))$
A4: $\cos(\exp(x)) +1 $
A5: $\cos(\exp(\sin(x)))$
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Last update: 2025-01
