CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Q293 Marksinitial_value_antiderivatives
CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Question 29 (Integrals)
Find F if F′(x)=1/(eˣ+1) and F(0)=ln(1/2).
✅ Step-by-Step Solution
Final Answer: F(x)=x−ln(1+eˣ).
- Write 1/(1+eˣ)=1−eˣ/(1+eˣ).
- Integrate to get F=x−ln(1+eˣ)+C. The initial value is −ln 2+C=−ln 2.
- Thus C=0 and F=x−ln(1+eˣ).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write 1/(1+eˣ)=1−eˣ/(1+eˣ).
- [2 marks] Integrate to get F=x−ln(1+eˣ)+C. The initial value is −ln 2+C=−ln 2.
- [0.5 marks] Thus C=0 and F=x−ln(1+eˣ).
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