Question Detail
Question
Given a is a positive constant and ∫ₐ^(3a) (3x-1)/x dx = 6+ln(1/2), find the value of a
Correct Answer
Option D is the correct answer.
Detailed Explanation
∫ₐ^(3a)(3-1/x)dx = 6a - ln3. Setting this equal to 6+ln(1/2) = 6-ln3 and matching the -ln3 terms directly gives 6a=6, so a=1.
Hint
Split into 3 - 1/x, integrate, and compare the resulting logarithmic term to ln(1/2).