NCERT Class 12 · Ch 7 Exercise 7.3 · Q10
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.3 Question 10
Evaluate \(\int \sin^{4}{\left(x \right)}\, dx\).
💡 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: \(\frac{3 x}{8} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32}\) + C.
- Work on each open interval where the original integrand is real and defined.
- Use sin⁴x=(3−4cos 2x+cos 4x)/8.
- An antiderivative is F(x)=\(\frac{3 x}{8} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32}\).
- Differentiate this expression to check that F′(x)=\(\sin^{4}{\left(x \right)}\). Add an arbitrary constant C on each domain component.
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