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NCERT Class 12 · Ch 7 Exercise 7.10 · Q15

NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 15

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \frac{\sin{\left(x \right)} - \cos{\left(x \right)}}{\sin{\left(x \right)} \cos{\left(x \right)} + 1}\, dx\) 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: \(0\)
  1. Reflect x↦π/2−x; the numerator changes sign and denominator stays unchanged.
  2. Thus I=−I and I=0; the denominator is positive throughout the interval.

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