Class 12 Integrals · Short Answer2 Marksdefinite_integration
Class 12 Maths · Integrals · Short Answer #147
Evaluate \(\int_0^{\pi/2}2^{\sin x}/(2^{\sin x}+2^{\cos x})dx\).
✅ Step-by-Step Solution
Final Answer: π/4
- Reflection x↦π/2−x interchanges sine and cosine in the numerator and denominator.
- Adding the equal integrals gives 2I=∫₀^(π/2)1dx=π/2.
- Therefore the integral equals π/4.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Reflection x↦π/2−x interchanges sine and cosine in the numerator and denominator.
- [1 mark] Adding the equal integrals gives 2I=∫₀^(π/2)1dx=π/2.
- [0.5 marks] Therefore the integral equals π/4.
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