Finding the Area Under a Curve (VCE SSCE Mathematical Methods): Flashcards

Net signed area under curve

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

$A = -\int_a^b f(x) \, dx$

Integral gives negative value but area must be positive

Reverse limits: $A = \int_b^a f(x) \, dx$

Split integral at crossing point, add absolute values

Sign of $f(x)$ in the given interval

Yes, area must always be positive

Whether curve is above or below x-axis

$A = \int_c^b f(x)dx + (-\int_a^c f(x)dx)$