Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration
Class 12 Maths · Integrals · Conceptual Answer #128
If ∫(ax+b)²dx=f(x)+C, give one possible f(x), valid also at a=0.
✅ Step-by-Step Solution
Final Answer: \(\frac{a^{2} x^{3}}{3} + a b x^{2} + b^{2} x\) + C
- Expand (ax+b)²=a²x²+2abx+b², then integrate each term. This works also when a=0; an arbitrary additive constant may be absorbed into C.
- Therefore the required integral is \(\frac{a^{2} x^{3}}{3} + a b x^{2} + b^{2} x\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Expand (ax+b)²=a²x²+2abx+b², then integrate each term. This works also when a=0; an arbitrary additive constant may be absorbed into C.
- [0.5 marks] Therefore the required integral is \(\frac{a^{2} x^{3}}{3} + a b x^{2} + b^{2} x\) + C.
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