Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration
Class 12 Maths · Integrals · Conceptual Answer #40
Evaluate \(\int \frac{1}{\sqrt{9 - 4 x^{2}}}\,dx\). Work for −3/2<x<3/2.
✅ Step-by-Step Solution
Final Answer: \(\frac{\operatorname{asin}{\left(\frac{2 x}{3} \right)}}{2}\) + C
- Write 9−4x²=9[1−(2x/3)²]. With u=2x/3 the integral is (1/2)∫du/√(1−u²)=(1/2)arcsin u+C.
- Therefore the required integral is \(\frac{\operatorname{asin}{\left(\frac{2 x}{3} \right)}}{2}\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write 9−4x²=9[1−(2x/3)²]. With u=2x/3 the integral is (1/2)∫du/√(1−u²)=(1/2)arcsin u+C.
- [0.5 marks] Therefore the required integral is \(\frac{\operatorname{asin}{\left(\frac{2 x}{3} \right)}}{2}\) + C.
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