Class 12 Integrals · Short Answer2 Marksdefinite_integration
Class 12 Maths · Integrals · Short Answer #49
Evaluate \(\int_1^2(1/x-1/(2x^2))e^{2x}dx\).
✅ Step-by-Step Solution
Final Answer: e⁴/4−e²/2
- Recognize the product derivative d[e^(2x)/(2x)]/dx=e^(2x)(1/x−1/(2x²)).
- The endpoint difference is e⁴/(2·2)−e²/(2·1).
- Therefore the integral equals e⁴/4−e²/2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Recognize the product derivative d[e^(2x)/(2x)]/dx=e^(2x)(1/x−1/(2x²)).
- [1 mark] The endpoint difference is e⁴/(2·2)−e²/(2·1).
- [0.5 marks] Therefore the integral equals e⁴/4−e²/2.
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