Class 12 Applications Of Integrals · Short Answer2 Marksarea_by_integration
Class 12 Maths · Applications Of Integrals · Short Answer #9
Find the area bounded by y=x², the x-axis, and x=−1,x=1.
✅ Step-by-Step Solution
Final Answer: \(\frac{2}{3}\) square units
- The parabola is on or above the x-axis; the specified vertical boundaries give limits −1,1. The strip widths are \(x^{2}\) for x∈\(\left[-1, 1\right]\).
- Primitive \(\frac{x^{3}}{3}\), endpoint difference \(\frac{2}{3}\).
- Therefore the area is \(\frac{2}{3}\) square units.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The parabola is on or above the x-axis; the specified vertical boundaries give limits −1,1. The strip widths are \(x^{2}\) for x∈\(\left[-1, 1\right]\).
- [1 mark] Primitive \(\frac{x^{3}}{3}\), endpoint difference \(\frac{2}{3}\).
- [0.5 marks] Therefore the area is \(\frac{2}{3}\) square units.
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