Integrals involving trigonometric substitution (HSC SSCE Mathematics Extension 1): Flashcards

Use $x = a \tan \theta$ for ellipse shape.

Use $x = a \sec \theta$, sometimes $a \tan \theta$.

Integral becomes $\int 4 \cos^2 \theta d\theta$.

Use $1 + \tan^2 \theta = \sec^2 \theta$.

Substitute $x=a \sin \theta$, then integrate.

To match $x$-limits to $\theta$-values.

Use $x=a\sec\theta$, or sometimes $a \tan \theta$.

Use $x=a\sin \theta$, transform integrand.

$x=a\sin\theta$, $x=a\tan\theta$, $x=a\sec\theta$.

Use $x=3 \sin \theta$, then integrate.