Question:

Given: Problem statement: Evaluate $\int_0^{\pi} \frac{x dx}{a^2 \cos^2 x + b^2 \sin^2 x}$.
Step 1: Apply Definite Integral Property (P4 / King Rule):
Write $I = \int_0^a f(a-x) dx$ and add to original integral $I$. [1.0 Mark]
Step 2: Simplify combined integral expression:
Cancel terms in numerator and denominator. [1.0 Mark]
Step 3: Substitute algebraic/trigonometric terms:
Divide by $\cos^2 x$ or apply half-angle substitution. [1.0 Mark]
Step 4: Execute Integration:
Evaluate standard anti-derivative. [1.0 Mark]
Step 5: Apply limits of integration:
Substitute upper and lower limits to state final answer. [1.0 Mark]
Conclusion: Integral evaluated.

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🎯 Official CBSE Marking Scheme:
Applying integral property P4: 1.0 Mark
Simplifying combined integrand: 1.0 Mark
Substituting trigonometric/algebraic terms: 1.0 Mark
Evaluating indefinite integral: 1.0 Mark
Evaluating final numerical result: 1.0 Mark