Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration
Class 12 Maths · Integrals · Conceptual Answer #35
Evaluate \(\int \frac{1}{4 x^{2} + 9}\,dx\). Work on each connected open interval where the real integrand is defined.
✅ Step-by-Step Solution
Final Answer: \(\frac{\operatorname{atan}{\left(\frac{2 x}{3} \right)}}{6}\) + C
- Use u=2x/3: dx=(3/2)du and 9+4x²=9(1+u²). Hence the integral is (1/6)arctan u+C.
- Therefore the required integral is \(\frac{\operatorname{atan}{\left(\frac{2 x}{3} \right)}}{6}\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Use u=2x/3: dx=(3/2)du and 9+4x²=9(1+u²). Hence the integral is (1/6)arctan u+C.
- [0.5 marks] Therefore the required integral is \(\frac{\operatorname{atan}{\left(\frac{2 x}{3} \right)}}{6}\) + C.
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