Final answer:
A trigonometric substitution of \(x=10\sin(\theta)\) is suggested for an integral containing \(\sqrt{100-x^2}\), using the Pythagorean identity to simplify the square root expression.
Step-by-step explanation:
When faced with an integral containing \(\sqrt{100-x^2}\), it is often beneficial to use a trigonometric substitution. Specifically, the substitution suggested is \(x=10\sin(\theta)\), where \(\theta\) is the new variable. This transformation leverages the Pythagorean identity \(\sin^2(\theta) + \cos^2(\theta) = 1\) to simplify the square root expression.
This change of variables will convert the integral into a form that is typically easier to evaluate and is a standard technique in calculus when dealing with integrals containing a square root of a sum or difference of squares.