Class 12 Integrals · Short Answer2 Marksindefinite_integration
Class 12 Maths · Integrals · Short Answer #53
Evaluate \(\int \frac{1}{\sqrt{- 2 x^{2} - 4 x + 5}}\,dx\). Work for |x+1|<√(7/2).
✅ Step-by-Step Solution
Final Answer: \(\frac{\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{14} \left(x + 1\right)}{7} \right)}}{2}\) + C
- Complete the square: 5−4x−2x²=7−2(x+1)².
- With u=√(2/7)(x+1), the integral becomes (1/√2)∫du/√(1−u²).
- Therefore the required integral is \(\frac{\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{14} \left(x + 1\right)}{7} \right)}}{2}\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Complete the square: 5−4x−2x²=7−2(x+1)².
- [1 mark] With u=√(2/7)(x+1), the integral becomes (1/√2)∫du/√(1−u²).
- [0.5 marks] Therefore the required integral is \(\frac{\sqrt{2} \operatorname{asin}{\left(\frac{\sqrt{14} \left(x + 1\right)}{7} \right)}}{2}\) + C.
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