Class 12 Integrals · Long Answer3 Marksdefinite_integration
Class 12 Maths · Integrals · Long Answer #168
Evaluate \(\int_0^4[|x|+|x-2|+|x-4|]dx\).
✅ Step-by-Step Solution
Final Answer: 20
- On [0,4], |x|+|x−4|=x+4−x=4.
- Therefore I=16+∫₀²(2−x)dx+∫₂⁴(x−2)dx.
- Each remaining triangle contributes 2, so I=16+2+2=20.
- Therefore the integral equals 20.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] On [0,4], |x|+|x−4|=x+4−x=4.
- [1 mark] Therefore I=16+∫₀²(2−x)dx+∫₂⁴(x−2)dx.
- [1 mark] Each remaining triangle contributes 2, so I=16+2+2=20.
- [0.5 marks] Therefore the integral equals 20.
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