Class 12 Integrals · Long Answer3 Marksdefinite_integration
Class 12 Maths · Integrals · Long Answer #87
Evaluate \(\int_0^{2\pi}dx/(1+e^{\sin x})\).
✅ Step-by-Step Solution
Final Answer: π
- Let I be the integral. Under reflection x↦2π−x, sin(2π−x)=−sin x.
- Thus I=∫₀^(2π)e^(sin x)/(1+e^(sin x))dx.
- Adding this to the original gives 2I=∫₀^(2π)1dx=2π.
- Therefore the integral equals π.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Let I be the integral. Under reflection x↦2π−x, sin(2π−x)=−sin x.
- [1 mark] Thus I=∫₀^(2π)e^(sin x)/(1+e^(sin x))dx.
- [1 mark] Adding this to the original gives 2I=∫₀^(2π)1dx=2π.
- [0.5 marks] Therefore the integral equals π.
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