NCERT Class 12 · Ch 7 Exercise 7.1 · Q21
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.1 Question 21
Evaluate \(\int \left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)\, dx\).
💡 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: C: \(\frac{2 x^{\frac{3}{2}}}{3} + 2 \sqrt{x}\) + C.
- Work for x>0.
- Use powers x^(1/2)+x^(−1/2), then increase each exponent by 1 and divide by it.
- An antiderivative is F(x)=\(\frac{2 x^{\frac{3}{2}}}{3} + 2 \sqrt{x}\).
- Differentiate this expression to check that F′(x)=\(\sqrt{x} + \frac{1}{\sqrt{x}}\). Add an arbitrary constant C on each domain component.
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