CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Q263 Marksindefinite_integrals
CBSE Class 12 Mathematics 2026 Main Paper 65/2/1 · Question 26 (Integrals)
Find \(\int\frac{x+2}{\sqrt{9x-x^2}}\,dx\).
✅ Step-by-Step Solution
Final Answer: −√(9x−x²)+(13/2) arcsin((2x−9)/9)+C on 0<x<9.
- Write x+2=−(9−2x)/2+13/2 and 9x−x²=(9/2)²−(x−9/2)².
- The first term integrates to −√(9x−x²). The second uses the standard arcsine integral after translating x by 9/2.
- Combine to obtain −√(9x−x²)+(13/2) arcsin((2x−9)/9)+C.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write x+2=−(9−2x)/2+13/2 and 9x−x²=(9/2)²−(x−9/2)².
- [2 marks] The first term integrates to −√(9x−x²). The second uses the standard arcsine integral after translating x by 9/2.
- [0.5 marks] Combine to obtain −√(9x−x²)+(13/2) arcsin((2x−9)/9)+C.
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