NCERT Class 12 · Ch 7 Exercise 7.10 · Q17
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 17
Evaluate \(\int\limits_{0}^{a} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}}\, dx\) 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: \(\frac{a}{2}\)
- Assume a>0. Reflect x↦a−x so the numerator becomes √(a−x).
- The two integrands sum to 1, giving 2I=a. At a=0 the interval collapses; for a<0 the displayed real-root integrand is not real on the intervening interval.
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