Class 12 Integrals · Long Answer3 Marksdefinite_integration
Class 12 Maths · Integrals · Long Answer #99
Evaluate \(\int_1^3[|x-1|+|x-2|+|x-3|]dx\).
✅ Step-by-Step Solution
Final Answer: 5
- On [1,3], |x−1|=x−1 and |x−3|=3−x; their sum is 2.
- Thus I=∫₁³2dx+∫₁²(2−x)dx+∫₂³(x−2)dx.
- The contributions are 4,1/2,1/2, giving I=5.
- Therefore the integral equals 5.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] On [1,3], |x−1|=x−1 and |x−3|=3−x; their sum is 2.
- [1 mark] Thus I=∫₁³2dx+∫₁²(2−x)dx+∫₂³(x−2)dx.
- [1 mark] The contributions are 4,1/2,1/2, giving I=5.
- [0.5 marks] Therefore the integral equals 5.
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