Class 12 Applications Of Integrals · Short Answer2 Marksarea_by_integration
Class 12 Maths · Applications Of Integrals · Short Answer #13
Sketch the region bounded by 2x+y=8, y=2,y=4 and the y-axis. Find its area using integration.
✅ Step-by-Step Solution
Final Answer: \(5\) square units
- The line is x=(8−y)/2 and the y-axis is x=0. At y=2,4 the line points are (3,2),(2,4). The strip widths are \(4 - \frac{y}{2}\) for y∈\(\left[2, 4\right]\).
- Primitive \(- \frac{y^{2}}{4} + 4 y\), endpoint difference \(5\).
- Therefore the area is \(5\) square units.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The line is x=(8−y)/2 and the y-axis is x=0. At y=2,4 the line points are (3,2),(2,4). The strip widths are \(4 - \frac{y}{2}\) for y∈\(\left[2, 4\right]\).
- [1 mark] Primitive \(- \frac{y^{2}}{4} + 4 y\), endpoint difference \(5\).
- [0.5 marks] Therefore the area is \(5\) square units.
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