Question Detail
Question
For ∫√(3-x²)dx, the best substitution is
Correct Answer
Option C is the correct answer.
Detailed Explanation
For integrals involving the form √(a²-x²), the standard trigonometric substitution is x = asinθ (or x = acosθ).In this integral, we have √(3-x²), which means a² = 3. Therefore, a = √3.The best substitution would be x = √3sinz (or x = √3cosz). Among the given options, x = √3sinz is the correct choice.
Hint
Recall the standard trigonometric substitutions for integrals involving expressions like √(a²-x²). Identify the value of 'a' in this case.