NCERT Class 12 · Ch 7 Exercise 7.10 · Q1
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 1
Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \cos^{2}{\left(x \right)}\, dx\) using definite-integral properties.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(\frac{\pi}{4}\)
- Reflection x↦π/2−x gives the same integral with sin²x.
- Adding yields 2I=∫₀^(π/2)(cos²x+sin²x)dx=π/2, hence I=π/4.
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