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NCERT Class 12 · Ch 7 Miscellaneous Exercise · Q26

NCERT Class 12 Maths · Chapter 7 Integrals · Miscellaneous Exercise Question 26

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \frac{\cos^{2}{\left(x \right)}}{4 \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}\, dx\).

💡 Concept Hints

  1. Identify the domain and the inner and outer functions, or the relevant one-sided limits.
  2. Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: \(\frac{\pi}{6}\)
  1. Put u=tan x. The transformed integrand is 1/[(1+u²)(1+4u²)]; use partial fractions.
  2. Partial fractions give −1/[3(1+u²)]+4/[3(1+4u²)].
  3. Integrate from u=0 to ∞: −π/6+π/3=π/6.

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All Questions in Integrals — Miscellaneous Exercise

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