Area of region bounded by two curves

Area bounded between \(2\) curves \(y = \mathrm{f}(x)\) and \(y = \mathrm{g}(x)\) from \(x = a\) to \(x = b\) is given by,

\[A = \int_{a}^{b} [\mathrm{f}(x) - \mathrm{g}(x)] \, \mathrm{d}x\]

Note that we always subtract the equation of the bottom curve from the equation of the top curve.
The underlying principle is that by so doing the resulting function is non-negative, and thus falls under the case where the resulting curve lies above the \(x\)-axis.

Similarly, the area bounded between \(2\) curves \(x = \mathrm{p}(y)\) and \(x = \mathrm{h}(y)\) is given by:

\[\int_{a}^{b} [\mathrm{h}(y) - \mathrm{p}(y)] \, \mathrm{d}y\]