To evaluate the integral ∫(9x√(4 - x²))dx, we can make use of the following substitution(s) to simplify the integral:
x = 2sinθ: This substitution is helpful because it converts the term involving the square root (√(4 - x²)) into a trigonometric function. This substitution is commonly used when dealing with integrals involving square roots of a quadratic expression.
x = 2tanθ: This substitution can also be useful as it converts the integral into a trigonometric function involving tangent. It can be used to simplify the integral and express it in terms of trigonometric functions.
So, the applicable substitutions for evaluating the integral are:
x = 2sinθ
x = 2tanθ
Note: The other options provided (0 = 2sinx, 00 = √(4 - x²), x = 2sece, Keypad Keyboard Shortcuts) are not relevant to evaluating this particular integral and can be disregarded.