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CBSE Class 12 Mathematics 2026 Main Paper 65/4/1 · Q335 Marksabsolute_value_area

CBSE Class 12 Mathematics 2026 Main Paper 65/4/1 · Question 33 (Applications Of Integrals)

Use integration to find the area between y=|x−6| and the x-axis for 4≤x≤8.
Area between the V-shaped graph and the x-axis from 4 to 8.
Area between the V-shaped graph and the x-axis from 4 to 8.

✅ Step-by-Step Solution

Final Answer: 4 square units.
  1. Split at x=6, where the expression changes from 6−x to x−6.
  2. Integrate 6−x on [4,6] and x−6 on [6,8]. Each integral equals 2.
  3. The two areas sum to 4.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Split at x=6, where the expression changes from 6−x to x−6.
  • [3 marks] Integrate 6−x on [4,6] and x−6 on [6,8]. Each integral equals 2.
  • [1 mark] The two areas sum to 4.

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