NCERT Class 12 · Ch 7 Exercise 7.2 · Q6
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 6
Evaluate \(\int \sqrt{a x + b}\, dx\).
💡 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: For a≠0: 2(ax+b)^(3/2)/(3a)+C on the real domain. For a=0,b≥0: x√b+C; for a=0,b<0 there is no real integrand.
- Work on each open interval where the original integrand is real and defined.
- u=ax+b, du=a dx, a≠0; integrate u^(1/2)du/a. If a=0,b≥0 the answer is x√b+C.
- An antiderivative is F(x)=\(\frac{2 \left(a x + b\right)^{\frac{3}{2}}}{3 a}\).
- Differentiate this expression to check that F′(x)=\(\sqrt{a x + b}\). Add an arbitrary constant C on each domain component.
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