NCERT Class 12 · Ch 7 Exercise 7.10 · Q11
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 11
Evaluate \(\int\limits_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \sin^{2}{\left(x \right)}\, dx\) 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: \(\frac{\pi}{2}\)
- The integrand is even, so I=2∫₀^(π/2)sin²x dx.
- Use sin²x=(1−cos 2x)/2 to get 2·π/4=π/2.
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