NCERT Class 12 · Ch 7 Exercise 7.2 · Q7
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 7
Evaluate \(\int x \sqrt{x + 2}\, dx\).
💡 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: \(\frac{2 \left(x + 2\right)^{\frac{5}{2}}}{5} - \frac{4 \left(x + 2\right)^{\frac{3}{2}}}{3}\) + C.
- Work on each open interval where the original integrand is real and defined.
- u=x+2, x=u−2; integrate (u−2)u^(1/2)du.
- An antiderivative is F(x)=\(\frac{2 \left(x + 2\right)^{\frac{5}{2}}}{5} - \frac{4 \left(x + 2\right)^{\frac{3}{2}}}{3}\).
- Differentiate this expression to check that F′(x)=\(x \sqrt{x + 2}\). Add an arbitrary constant C on each domain component.
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