Applications of Integration : Area under Graph

IB AA SL: core and optional content

Core: areas by integration with respect to x. Optional: horizontal-strip methods with respect to y.

For a continuous curve \(y=f(x)\) on \([a,b]\), the definite integral gives signed area. Geometric area is \(\int_a^b |f(x)|\,\mathrm dx\), evaluated by splitting where the curve changes sign. For two boundaries, integrate their positive separation, choosing vertical or horizontal strips to suit the region.