NCERT Class 12 · Ch 7 Exercise 7.10 · Q12
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 12
Evaluate \(\int\limits_{0}^{\pi} \frac{x}{\sin{\left(x \right)} + 1}\, dx\) 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: \(\pi\)
- Reflect x↦π−x and add: 2I=π∫₀^πdx/(1+sin x).
- A primitive of 1/(1+sin x) is −cos x/(1+sin x), valid even at π/2. Its endpoint difference is 2, so I=π.
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