Medium Practice — Set 2

Quick Recap — Definite Integral Properties & Area

• $\displaystyle\int_0^a f(x)\,dx=\int_0^a f(a-x)\,dx$ (the ``king'' property); useful for $\tfrac{\sin}{\sin+\cos}$-type integrals.
• $\displaystyle\int_{-a}^a$: odd $\to0$, even $\to2\int_0^a$.
• Area under $y=f(x)\ge0$ from $a$ to $b$ is $\displaystyle\int_a^b f\,dx$; between two curves, $\int(\text{upper}-\text{lower})$.
• Split at points where $|f|$ changes sign.