Class 12 Integrals · Short Answer2 Marksproduct_derivative
Class 12 Maths · Integrals · Short Answer #139
Find one function f satisfying \(\int[(x-1)/x^2]e^x dx=e^x f(x)+C\), x≠0.
✅ Step-by-Step Solution
Final Answer: One choice is f(x)=1/x; generally f(x)=1/x+K e^(−x).
- Differentiate e^x/x to get e^x(1/x−1/x²)=e^x(x−1)/x².
- Hence e^x f=e^x/x+K on each connected interval.
- A valid choice is f=1/x; the full family is 1/x+K e^(−x).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Differentiate e^x/x to get e^x(1/x−1/x²)=e^x(x−1)/x².
- [1 mark] Hence e^x f=e^x/x+K on each connected interval.
- [0.5 marks] A valid choice is f=1/x; the full family is 1/x+K e^(−x).
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