Given: Problem statement: Evaluate $\int_0^{\pi} \frac{x \sin x}{1 + \cos^2 x} dx$. Step 1: Apply definite integral property / partial fractions: Apply king property $\int_0^a f(x) dx = \int_0^a f(a-x) dx$ or partial fraction decomposition. [1.0 Mark] Step 2: Integrate transformed functions: Compute anti-derivative or evaluate simplified definite integral. [1.0 Mark] Step 3: Evaluate limits and state final answer: Substitute limits of integration to obtain numerical/algebraic result. [1.0 Mark] Conclusion: Result evaluated successfully.
--- 🎯 Official CBSE Marking Scheme: Applying integral property / substitution: 1.0 Mark Evaluating indefinite/definite integral: 1.0 Mark Substituting limits and final answer: 1.0 Mark
Correct Answer:
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