5.3 The Fundamental Theorem of Calculus

Lecture

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Lecture notes

1. FTC #1

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

2. FTC #2

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int _{a}^{b}f(x)dx=F(b)-F(a)} where Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {d}{dx}}F(x)=f(x)}