Question Detail
Question
Given a is a positive constant and ∫ₐ^(3a) (2x+1)/x dx = ln12, find the exact value of a
Correct Answer
Option B is the correct answer.
Detailed Explanation
∫ₐ^(3a) (2+1/x)dx = 4a + ln(3a/a) = 4a+ln3. Setting 4a+ln3=ln12 gives 4a=ln4, so a=(1/4)ln4.
Hint
Split the integrand into 2 + 1/x and integrate each piece separately before solving for a.