Class 12 Applications Of Integrals · Short Answer2 Marksarea_by_integration
Class 12 Maths · Applications Of Integrals · Short Answer #37
Find the area bounded by y=x²,x=2,x=3 and the x-axis.
✅ Step-by-Step Solution
Final Answer: \(\frac{19}{3}\) square units
- The parabola is positive throughout [2,3], so the strip height is x². The strip widths are \(x^{2}\) for x∈\(\left[2, 3\right]\).
- Primitive \(\frac{x^{3}}{3}\), endpoint difference \(\frac{19}{3}\).
- Therefore the area is \(\frac{19}{3}\) square units.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The parabola is positive throughout [2,3], so the strip height is x². The strip widths are \(x^{2}\) for x∈\(\left[2, 3\right]\).
- [1 mark] Primitive \(\frac{x^{3}}{3}\), endpoint difference \(\frac{19}{3}\).
- [0.5 marks] Therefore the area is \(\frac{19}{3}\) square units.
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