NCERT Class 12 · Ch 7 Miscellaneous Exercise · Q33
NCERT Class 12 Maths · Chapter 7 Integrals · Miscellaneous Exercise Question 33
Evaluate \(\int\limits_{0}^{1} x e^{x}\, dx\).
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(1\)
- Work on each open interval where the original integrand is real and defined.
- Use integration by parts with u=x, dv=eˣdx.
- An antiderivative is F(x)=\(\left(x - 1\right) e^{x}\).
- At the upper and lower limits, F(b)=\(0\) and F(a)=\(-1\).
- By the fundamental theorem (using one-sided limits for any integrable endpoint), I=F(b)−F(a)=\(1\).
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