Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration
Class 12 Maths · Integrals · Conceptual Answer #131
Evaluate \(\int \operatorname{acos}{\left(\sin{\left(x \right)} \right)}\,dx\). Work for −π/2<x<π/2.
✅ Step-by-Step Solution
Final Answer: \(- \frac{x^{2}}{2} + \frac{\pi x}{2}\) + C
- On −π/2<x<π/2, arccos(sin x)=π/2−x by the principal range of arccos. Integrate this linear function.
- Therefore the required integral is \(- \frac{x^{2}}{2} + \frac{\pi x}{2}\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] On −π/2<x<π/2, arccos(sin x)=π/2−x by the principal range of arccos. Integrate this linear function.
- [0.5 marks] Therefore the required integral is \(- \frac{x^{2}}{2} + \frac{\pi x}{2}\) + C.
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