NCERT Class 12 · Ch 8 Exercise 8.1 · Q3
NCERT Class 12 Maths · Chapter 8 Applications Of Integrals · Exercise 8.1 Question 3
Find the first-quadrant area bounded by x²+y²=4, x=0 and x=2.
💡 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: A: π square units.
- In the first quadrant, y=√(4−x²), with 0≤x≤2.
- The area is ∫₀²√(4−x²)dx. Substituting x=2sin θ gives 4∫₀^(π/2)cos²θ dθ=π.
- This is also one quarter of the radius-2 circle: π·2²/4=π, option A.
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