Tutorial Week 3
Trigonometric Substitution (Trig Sub)
The method of Trig sub takes advantage of your trig identities to simplify integrals and in a way, it’s just fancy and strategic U-sub. Refer to the following table for which substitution to use:
Expression |
\(\sqrt{a^2-x^2}\) |
\(\sqrt{a^2+x^2}\) |
\(\sqrt{x^2-a^2}\) |
Substitution |
\(x=a\sin \theta\) |
\(x=a\tan \theta\) |
\(x=a\sec \theta\) |
Domain |
\(\theta \in [-\frac{\pi}{2}, \frac{\pi}{2}]\) |
\(\theta \in (-\frac{\pi}{2}, \frac{\pi}{2})\) |
\(\theta \in [0, -\frac{\pi}{2}) \cup (\frac{\pi}{2}, \pi]\) |
Q1: Integrate \(\int \frac{1}{\sqrt{x^2 + 10x + 27}} dx\).
