NCERT Class 12 · Ch 7 Exercise 7.2 · Q8
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 8
Evaluate \(\int x \sqrt{2 x^{2} + 1}\, dx\).
💡 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: \(\frac{\left(2 x^{2} + 1\right)^{\frac{3}{2}}}{6}\) + C.
- Work on each open interval where the original integrand is real and defined.
- u=1+2x², du=4x dx.
- An antiderivative is F(x)=\(\frac{\left(2 x^{2} + 1\right)^{\frac{3}{2}}}{6}\).
- Differentiate this expression to check that F′(x)=\(x \sqrt{2 x^{2} + 1}\). Add an arbitrary constant C on each domain component.
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