Class 12 Integrals · Long Answer3 Marksdefinite_integration
Class 12 Maths · Integrals · Long Answer #97
Evaluate \(\int_{-\pi/2}^{\pi/2}\cos x/(1+e^x)dx\).
✅ Step-by-Step Solution
Final Answer: 1
- Write the integral as the sum over [−π/2,0] and [0,π/2].
- In the first part substitute x=−t. Since cosine is even, its integrand becomes e^t cos t/(1+e^t).
- Adding the second part leaves ∫₀^(π/2)cos t dt=1.
- Therefore the integral equals 1.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write the integral as the sum over [−π/2,0] and [0,π/2].
- [1 mark] In the first part substitute x=−t. Since cosine is even, its integrand becomes e^t cos t/(1+e^t).
- [1 mark] Adding the second part leaves ∫₀^(π/2)cos t dt=1.
- [0.5 marks] Therefore the integral equals 1.
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