Mr. Integral
Math notes/Calculus II/Geometry and Physical Applications

Area Between Curves and Average Values — Cheat sheet

CHEAT SHEET   ·   FREE

Choose “Save as PDF” in the print dialog.
On this page

Core rule

A=∫ab∣f−g∣dx,A=\int_a^b|f-g|dx, favg=∫abf(x)dxb−a.f_{\rm avg}=\frac{\int_a^bf(x)dx}{b-a}.

Watch for

Split where boundaries cross. Area has square units; an average has the same units as the original function.