Question Detail
Question
By Wallis' formula, evaluate ∫₀^(π/2) cos⁴ x dx.
Correct Answer
Option C is the correct answer.
Detailed Explanation
Wallis' formula for ∫₀^(π/2) cosⁿ x dx (where n is an even integer) is:[(n-1)!! / n!!] * (π/2).Here, n = 4.(4-1)!! = 3!! = 3 * 1 = 3.4!! = 4 * 2 = 8.So, the integral is (3/8) * (π/2) = 3π/16.
Hint
Apply Wallis' formula for a single power of cosine: [(n-1)!! / n!!] * (π/2) when n is even.