Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration
Class 12 Maths · Integrals · Conceptual Answer #127
Evaluate \(\int 3 \sqrt{x} + \frac{1}{\sqrt{x}}\,dx\). Work for x>0.
✅ Step-by-Step Solution
Final Answer: \(2 x^{\frac{3}{2}} + 2 \sqrt{x}\) + C
- Integrate powers: ∫(3x^(1/2)+x^(−1/2))dx=2x^(3/2)+2x^(1/2)+C.
- Therefore the required integral is \(2 x^{\frac{3}{2}} + 2 \sqrt{x}\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Integrate powers: ∫(3x^(1/2)+x^(−1/2))dx=2x^(3/2)+2x^(1/2)+C.
- [0.5 marks] Therefore the required integral is \(2 x^{\frac{3}{2}} + 2 \sqrt{x}\) + C.
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