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CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Q345 Markscircle_area

CBSE Class 12 Mathematics 2026 Main Paper 65/5/3 · Question 34 (Applications Of Integrals)

Sketch x²+y²=25. Find by integration the area of the minor segment cut off by x=5/2.
A circle of radius 5 with the minor segment to the right of x=5/2 shaded.
A circle of radius 5 with the minor segment to the right of x=5/2 shaded.

✅ Step-by-Step Solution

Final Answer: 25π/3−25√3/4 square units.
  1. The minor segment lies to the right of x=5/2, so its area is 2∫ from 5/2 to 5 of √(25−x²) dx.
  2. An antiderivative after the factor of two is x√(25−x²)+25 arcsin(x/5).
  3. Evaluate at 5 and 5/2 to get 25π/2−25π/6−25√3/4.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] The minor segment lies to the right of x=5/2, so its area is 2∫ from 5/2 to 5 of √(25−x²) dx.
  • [3 marks] An antiderivative after the factor of two is x√(25−x²)+25 arcsin(x/5).
  • [1 mark] Evaluate at 5 and 5/2 to get 25π/2−25π/6−25√3/4.

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