Class 12 Integrals · Short Answer2 Marksdefinite_integration
Class 12 Maths · Integrals · Short Answer #149
Evaluate \(\int_{-\pi/2}^{\pi/2}\sin^5x\,dx\).
✅ Step-by-Step Solution
Final Answer: 0
- Since sin(−x)=−sin x, sin⁵x is odd and continuous.
- The integral of an odd continuous function over symmetric limits is 0.
- Therefore the integral equals 0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Since sin(−x)=−sin x, sin⁵x is odd and continuous.
- [1 mark] The integral of an odd continuous function over symmetric limits is 0.
- [0.5 marks] Therefore the integral equals 0.
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