NCERT Class 12 · Ch 7 Exercise 7.2 · Q11
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 11
Evaluate \(\int \frac{x}{\sqrt{x + 4}}\, dx\).
💡 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: \(\frac{2 \left(x + 4\right)^{\frac{3}{2}}}{3} - 8 \sqrt{x + 4}\) + C.
- Work on each open interval where the original integrand is real and defined.
- u=x+4, x=u−4; integrate u^(1/2)−4u^(−1/2), x>0 as stated.
- An antiderivative is F(x)=\(\frac{2 \left(x + 4\right)^{\frac{3}{2}}}{3} - 8 \sqrt{x + 4}\).
- Differentiate this expression to check that F′(x)=\(\frac{x}{\sqrt{x + 4}}\). Add an arbitrary constant C on each domain component.
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