Question

Choose the substitution(s) that are helpful in evaluating the integral Answer 9x√/4 – x²dx. Do not actually evaluate the integral. Select all answers that apply. O x = 2sine 00=4-x² 0 = 2sinx 00=√4-x² x = 2sece x = 2tan Keypad Keyboard Shortcuts

Answer 1

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.