5.3 The Fundamental Theorem of Calculus

Lecture

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Lecture notes

1. FTC #1

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

2. FTC #2

$\int _{a}^{b}f(x)dx=F(b)-F(a)$
Where ${\frac {d}{dx}}\left[F(x)\right]=f(x)$. $F(x)$ is called the antiderivative of $f(x)$

Solutions

Mr. V solutions: 8, 20, 28

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