CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Q263 Marksintegration_by_parts
CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Question 26 (Integrals)
Evaluate \(\int_0^1 \ln(1+x^2)\,dx\).
✅ Step-by-Step Solution
Final Answer: ln 2−2+π/2
- Integrate by parts with u=ln(1+x²) and dv=dx.
- The result is ln 2−2∫₀¹ x²/(1+x²) dx. Use x²/(1+x²)=1−1/(1+x²) and evaluate to get 1−π/4 for the integral.
- Hence the value is ln 2−2+π/2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Integrate by parts with u=ln(1+x²) and dv=dx.
- [2 marks] The result is ln 2−2∫₀¹ x²/(1+x²) dx. Use x²/(1+x²)=1−1/(1+x²) and evaluate to get 1−π/4 for the integral.
- [0.5 marks] Hence the value is ln 2−2+π/2.
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