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NCERT Class 12 · Ch 7 Exercise 7.10 · Q4

NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 4

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \frac{\cos^{5}{\left(x \right)}}{\sin^{5}{\left(x \right)} + \cos^{5}{\left(x \right)}}\, dx\) using definite-integral properties.

💡 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: \(\frac{\pi}{4}\)
  1. Reflect x↦π/2−x; the numerator swaps sine and cosine while the denominator stays the same.
  2. Adding the original and reflected integrands gives 1. Thus 2I=π/2 and I=π/4.

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