5.3 The Fundamental Theorem of Calculus

Lecture

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Lecture notes

1. FTC #1

${\frac {d}{dx}}\left[\int _{a(x)}^{b(x)}f(t)\,dt\right]=b'(x)\cdot f(b(x))-a'(x)\cdot f(a(x))$

2. FTC #2

$\int _{a}^{b}f(x)\,dx=F(b)-F(a)$
Where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{d}{dx}\left[F(x)\right]=f(x)} and $F(x)$ is called the antiderivative of $f(x)$

Solutions

Mr. V solutions: 8, 20, 28

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Pending

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