Math basics › Calculus II
Trig substitution
Spot the square root
√(a² − x²), √(a² + x²) or √(x² − a²) inside an integral is the signal. Each one matches a Pythagorean identity.
Which substitution
√(a² − x²): x = a sin θ. √(a² + x²): x = a tan θ. √(x² − a²): x = a sec θ. Each turns the root into a single trig function.
Change dx too
If x = a sin θ, then dx = a cos θ dθ. Forgetting to convert the dx is the most common slip.
Getting back to x
Draw a right triangle from your substitution, label its sides, and read the other trig functions off it.