Which trigonometric substitution involving the sine function is standard for an integral containing the term √(a² - x²)?

x = a sin θ

This substitution relies on the Pythagorean identity 1 - sin²θ = cos²θ to transform radical expressions into simpler trigonometric terms. By setting x = a sin θ, the expression √(a² - x²) simplifies directly to a cos θ, which is significantly easier to integrate. A helpful way to remember this is that the subtraction within the square root mirrors the subtraction found in the identity for cosine.