Sketch the region and solve for all relevant intersections. Choose strips that give the simplest boundaries.
\(A=\int_a^b(\text{upper}\hspace{0.5em}-\text{lower})\,\mathrm dx\)
\(A=\int_c^d(\text{right}\hspace{0.5em}-\text{left})\,\mathrm dy\)
A line and a curve: the curve is the upper graph between the two intersection points.
Two curves: the same rule — solve \(f(x)=g(x)\) for the limits, then integrate the difference.
Use limits in the integration variable. Check the boundary order on each interval and split where it changes. Crossing an axis alone does not require a split.
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