Class 12 Integrals · Short Answer2 Marksdefinite_integration
Class 12 Maths · Integrals · Short Answer #46
Evaluate \(\int_0^1x^2e^x dx\).
✅ Step-by-Step Solution
Final Answer: e−2
- Integrate by parts with u=x²,dv=e^x dx: I=[x²e^x]₀¹−2∫₀¹xe^x dx.
- A second integration by parts gives primitive e^x(x²−2x+2). Its endpoint difference is e−2.
- Therefore the integral equals e−2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Integrate by parts with u=x²,dv=e^x dx: I=[x²e^x]₀¹−2∫₀¹xe^x dx.
- [1 mark] A second integration by parts gives primitive e^x(x²−2x+2). Its endpoint difference is e−2.
- [0.5 marks] Therefore the integral equals e−2.
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