CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Q293 Marksabsolute_value_integrals
CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Question 29 (Integrals)
Evaluate \(\int_1^3(|x-1|+|x-2|+|x-3|)\,dx\).
✅ Step-by-Step Solution
Final Answer: 5.
- On [1,3], |x−1|+|x−3|=2.
- The remaining |x−2| integrates to 1 by symmetry around 2.
- Add the integral of 2, which is 4, to get 5.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] On [1,3], |x−1|+|x−3|=2.
- [2 marks] The remaining |x−2| integrates to 1 by symmetry around 2.
- [0.5 marks] Add the integral of 2, which is 4, to get 5.
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