Introduction to trigonometric substitution (video) | Khan Academy

Trig Substitution

Reference Triangle

Consider the following integral $\int \frac{1}{\sqrt{4-x^2}}dx$

Denominator looks like Pythagorean Theorem

• We get $\sin \theta = \frac{x}{2}$ and $\cos \theta = \frac{\sqrt{4-x^2}}{2}$
• Rearranging the equations, we get $x = 2 \sin \theta$, which means $dx = 2 cos \theta d \theta$