Class 12 Applications Of Integrals · Short Answer2 Marksarea_by_integration
Class 12 Maths · Applications Of Integrals · Short Answer #14
Find by integration the area enclosed by y=|x−1| and y=1.
✅ Step-by-Step Solution
Final Answer: \(1\) square units
- The intersections are (0,1),(2,1), and the V-vertex is (1,0). On [0,1] the lower graph is 1−x; on [1,2] it is x−1. The strip widths are \(x\) for x∈\(\left[0, 1\right]\); \(2 - x\) for x∈\(\left[1, 2\right]\).
- Primitive \(\frac{x^{2}}{2}\), endpoint difference \(\frac{1}{2}\); Primitive \(- \frac{x^{2}}{2} + 2 x\), endpoint difference \(\frac{1}{2}\).
- Therefore the area is \(1\) square units.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The intersections are (0,1),(2,1), and the V-vertex is (1,0). On [0,1] the lower graph is 1−x; on [1,2] it is x−1. The strip widths are \(x\) for x∈\(\left[0, 1\right]\); \(2 - x\) for x∈\(\left[1, 2\right]\).
- [1 mark] Primitive \(\frac{x^{2}}{2}\), endpoint difference \(\frac{1}{2}\); Primitive \(- \frac{x^{2}}{2} + 2 x\), endpoint difference \(\frac{1}{2}\).
- [0.5 marks] Therefore the area is \(1\) square units.
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