NCERT Class 12 · Ch 7 Exercise 7.6 · Q23
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.6 Question 23
Evaluate \(\int x^{2} e^{x^{3}}\, dx\).
💡 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: A: \(\frac{e^{x^{3}}}{3}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Put u=x³, du=3x²dx; integrate eᵘdu/3.
- An antiderivative is F(x)=\(\frac{e^{x^{3}}}{3}\).
- Differentiate this expression to check that F′(x)=\(x^{2} e^{x^{3}}\). Add an arbitrary constant C on each domain component.
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