Final answer:
A trigonometric substitution such as x = 10sin(θ) or x = 10cos(θ) is suggested for an integral containing the expression √(100-x²), because it simplifies the square root and facilitates easier integration using standard trigonometric integrals.
Step-by-step explanation:
For an integral containing the expression √(100-x²), the suggested change of variables would be to use a trigonometric substitution. Specifically, you could use the substitution x = 10sin(θ) or x = 10cos(θ), which simplifies the square root based on the identity sin²(θ) + cos²(θ) = 1. This change of variables will transform the integral into a form that involves trigonometric functions, which are generally easier to integrate.
In this case, if we choose x = 10sin(θ), then dx = 10cos(θ)dθ. Substituting these into the integral will give us an integral in terms of θ, which does not contain any square roots and can be evaluated using standard trigonometric integrals.