Area Under/Between Curves (Leaving Cert Mathematics): Flashcards

Definite integration

$\int_a^b f(x) \, dx$

Net area between curve and $x$-axis

When $f(x) \geq 0$ for all $x$ in $[a,b]$

Negative of area (integral negative)

Positive area minus negative area

Set up integral with $f(x)$ and $[a,b]$

Find antiderivative $F(x)$ of $f(x)$

$F(b) - F(a)$

Take absolute value: $|\int_a^b f(x) dx|$

$\int_a^b [f(x)-g(x)]dx$ where $f(x) \geq g(x)$

Integrate each part separately, use absolute values

Distance from 0 (magnitude/length)