Class 12 Integrals · Short Answer2 Marksindefinite_integration
Class 12 Maths · Integrals · Short Answer #142
Evaluate \(\int \frac{\cos{\left(\sqrt{x} \right)}}{\sqrt{x}}\,dx\). Work for x>0.
✅ Step-by-Step Solution
Final Answer: \(2 \sin{\left(\sqrt{x} \right)}\) + C
- Set u=√x, so dx/√x=2du.
- The integral becomes 2∫cos u du=2sin u+C; replace u=√x.
- Therefore the required integral is \(2 \sin{\left(\sqrt{x} \right)}\) + C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Set u=√x, so dx/√x=2du.
- [1 mark] The integral becomes 2∫cos u du=2sin u+C; replace u=√x.
- [0.5 marks] Therefore the required integral is \(2 \sin{\left(\sqrt{x} \right)}\) + C.
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