NCERT Class 12 · Ch 8 Exercise 8.1 · Q2
NCERT Class 12 Maths · Chapter 8 Applications Of Integrals · Exercise 8.1 Question 2
Find the area bounded by x²/4+y²/9=1.
💡 Concept Hints
- Sketch the region, choose a vertical or horizontal strip, and find all sign changes.
- Express its area as an integral of upper minus lower (or right minus left), splitting where necessary.
✅ Step-by-Step Solution
Final Answer: 6π square units.
- The ellipse is symmetric about both axes, with upper branch y=3√(1−x²/4).
- Its complete area is 4∫₀^2 3√(1−x²/4) dx.
- Put x=2sin θ, dx=2cos θ dθ, with θ from 0 to π/2. The area becomes 24∫₀^(π/2)cos²θ dθ.
- Using ∫₀^(π/2)cos²θ dθ=π/4 gives area 6π.
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