CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Q345 Marksellipse_area
CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Question 34 (Applications Of Integrals)
Sketch 100x²+25y²=2500 and use integration to find the enclosed area.
✅ Step-by-Step Solution
Final Answer: 50π square units.
- Divide by 2500 to obtain the ellipse x²/25+y²/100=1, with semiaxes 5 and 10.
- The upper branch is 2√(25−x²). Integrate it from 0 to 5 and multiply by four.
- The quarter-circle integral of √(25−x²) is 25π/4, giving 50π.
📋 CBSE Stepwise Marking Scheme
- [1 mark] Divide by 2500 to obtain the ellipse x²/25+y²/100=1, with semiaxes 5 and 10.
- [3 marks] The upper branch is 2√(25−x²). Integrate it from 0 to 5 and multiply by four.
- [1 mark] The quarter-circle integral of √(25−x²) is 25π/4, giving 50π.
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