Area between a curve and a line (AQA A-Level Mathematics): Flashcards

Integrate difference of functions over intersection interval

Find intersection points by solving $f(x) = g(x)$

$\int_a^b |f(x) - g(x)| dx$

When $f(x) \geq g(x)$ over entire interval

Split integral at crossing point(s)

Evaluate the definite integral

$y = x^2$ and $y = x + 2$

$x = -1$ and $x = 2$

$\int_{-1}^2 ((x+2) - x^2) dx$

$\frac{9}{2}$ or $4.5$ square units