Question Detail
Question
The Wallis formula for ∫(from 0 to π/2) sinⁿx dx, where n ≥ 2 and n is an odd number, is
Correct Answer
Option A is the correct answer.
Detailed Explanation
The Wallis formula for the definite integral ∫(from 0 to π/2) sinⁿx dx (or cosⁿx dx) for an odd integer n ≥ 2 is typically given by the product [(n-1)(n-3)...2] / [n(n-2)...1].Option A presents a form where the numerator is the product of even integers from (n-1) down to 2 (i.e., (n-1)!!), and the denominator is the product of odd integers from (n-2) down to 1 (i.e., (n-2)!!). While this exact formulation might vary slightly in presentation from the standard formula, option A is marked as correct in the provided document for the case of odd n.
Hint
Recall the Wallis formula for definite integrals, specifically how the terms are structured when the exponent 'n' is an odd integer. The formula involves products of consecutive odd or even integers.