NCERT Class 12 · Ch 7 Exercise 7.10 · Q14
NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 14
Evaluate \(\int\limits_{0}^{2 \pi} \cos^{5}{\left(x \right)}\, dx\) using definite-integral properties.
💡 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: \(0\)
- Split [0,2π] into [0,π] and [π,2π].
- The substitution x=u+π in the second part gives cos⁵(u+π)=−cos⁵u, so they cancel.
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