NCERT Class 12 · Ch 7 Exercise 7.3 · Q2
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.3 Question 2
Evaluate \(\int \sin{\left(3 x \right)} \cos{\left(4 x \right)}\, dx\).
💡 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: \(\frac{\cos{\left(x \right)}}{2} - \frac{\cos{\left(7 x \right)}}{14}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Use sin A cos B=[sin(A+B)+sin(A−B)]/2.
- An antiderivative is F(x)=\(\frac{\cos{\left(x \right)}}{2} - \frac{\cos{\left(7 x \right)}}{14}\).
- Differentiate this expression to check that F′(x)=\(\sin{\left(3 x \right)} \cos{\left(4 x \right)}\). Add an arbitrary constant C on each domain component.
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