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CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Q325 Marksdefinite_integral_symmetry

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2 · Question 32 (Integrals)

Evaluate \(\int_0^{\pi/2}\frac{\sin^2 x}{1+\sin x\cos x}\,dx\).

✅ Step-by-Step Solution

Final Answer: π/(3√3).
  1. Reflect x to π/2−x and add to obtain twice the integral as ∫₀^(π/2) dx/(1+sin x cos x).
  2. Set t=tan x. The resulting integral is ∫₀^∞ dt/(t²+t+1).
  3. Complete the square and evaluate: (2/√3)[arctan((2t+1)/√3)]₀^∞=2π/(3√3). Halve the result.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Reflect x to π/2−x and add to obtain twice the integral as ∫₀^(π/2) dx/(1+sin x cos x).
  • [3 marks] Set t=tan x. The resulting integral is ∫₀^∞ dt/(t²+t+1).
  • [1 mark] Complete the square and evaluate: (2/√3)[arctan((2t+1)/√3)]₀^∞=2π/(3√3). Halve the result.

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All Questions in CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/2

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38

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