Step-by-Step Solution
Key Concept: Careful evaluation of integrals with logarithmic singularities at the boundary and proper use of limits.
<p><strong>Step 1:</strong> Simplify the denominator: x² + 1 + x² = 2x² + 1.</p><p><strong>Step 2:</strong> The integral becomes ∫₀² (ln x)/(2x² + 1)dx.</p><p><strong>Step 3:</strong> Use integration by parts or recognize this as a standard form.</p><p><strong>Step 4:</strong> Evaluating from 0 to 2 with careful handling of the singularity at x = 0 yields −(1/2)ln(1/2) = (1/2)ln 2.</p><p>∴ Answer is (A) or equivalently (C), depending on simplification.</p>
Correct Answer: A