NCERT Class 12 · Ch 7 Exercise 7.3 · Q1
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.3 Question 1
Evaluate \(\int \sin^{2}{\left(2 x + 5 \right)}\, dx\).
💡 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: \(\frac{x}{2} - \frac{\sin{\left(4 x + 10 \right)}}{8}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Use sin²u=(1−cos 2u)/2.
- An antiderivative is F(x)=\(\frac{x}{2} - \frac{\sin{\left(4 x + 10 \right)}}{8}\).
- Differentiate this expression to check that F′(x)=\(\sin^{2}{\left(2 x + 5 \right)}\). Add an arbitrary constant C on each domain component.
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