Trigonometric Substitution

This animation displays the graphs of the three standard trigonometric substitution forms ($a^2 - x^2$, $a^2 + x^2$, and $x^2 - a^2$) in distinct colors, highlighting key points like peaks and crossings at $x = \pm a$. Beside each curve, the corresponding trigonometric substitution, differential, and Pythagorean identity are shown to illustrate the mathematical justification for each case.