5.3 The Fundamental Theorem of Calculus

Lecture

• Link

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 ${\frac {d}{dx}}\left[F(x)\right]=f(x)$ and $F(x)$ is called the antiderivative of $f(x)$

Solutions

Mr. V solutions: 8, 20, 28

7 8 9 10 11 13 15 17

Pending

1 3 5

25 27 28 29 31 33 35 37 39 41 53