Question Detail
Question
Using the Wallis formula the integral of ∫0π/2 cos3x dx is...
Correct Answer
Option B is the correct answer.
Detailed Explanation
The Wallis formula for definite integrals of the form ∫0π/2 cosnx dx (or sinnx dx) is:If n is an odd integer (n ≥ 1), then ∫0π/2 cosnx dx = [ (n-1)/n ] * [ (n-3)/(n-2) ] * ... * (2/3).In this problem, n=3, which is an odd integer.Applying the Wallis formula:∫0π/2 cos3x dx = ( (3-1)/3 )∫0π/2 cos3x dx = (2/3)This matches option B.
Hint
The Wallis formula is used for definite integrals of powers of sine or cosine from 0 to π/2. For odd powers 'n', the formula simplifies to a product of fractions starting from (n-1)/n and reducing by 2 in numerator and denominator until (2/3).