NCERT Class 12 · Ch 7 Exercise 7.2 · Q27
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 27
Evaluate \(\int \sqrt{\sin{\left(2 x \right)}} \cos{\left(2 x \right)}\, dx\).
💡 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: \(\frac{\sin^{\frac{3}{2}}{\left(2 x \right)}}{3}\) + C.
- Work on each open interval where the original integrand is real and defined.
- u=sin 2x, du=2cos 2x dx; use intervals sin 2x≥0.
- An antiderivative is F(x)=\(\frac{\sin^{\frac{3}{2}}{\left(2 x \right)}}{3}\).
- Differentiate this expression to check that F′(x)=\(\sqrt{\sin{\left(2 x \right)}} \cos{\left(2 x \right)}\). Add an arbitrary constant C on each domain component.
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