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CBSE Class 12 Mathematics 2026 Main Paper 65/4/2 · Q335 Marksabsolute_value_area

CBSE Class 12 Mathematics 2026 Main Paper 65/4/2 · Question 33 (Applications Of Integrals)

Use integration to find the area bounded by y=x|x|, the x-axis and the lines x=−2 and x=2.
The graph of y=x|x| and the two shaded areas between x=−2 and x=2.
The graph of y=x|x| and the two shaded areas between x=−2 and x=2.

✅ Step-by-Step Solution

Final Answer: 16/3 square units.
  1. The graph is below the axis on [−2,0] and above on [0,2].
  2. Integrate the magnitude x² over both intervals. By symmetry this is twice the integral on [0,2].
  3. Thus the total is 2[x³/3]₀²=16/3.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] The graph is below the axis on [−2,0] and above on [0,2].
  • [3 marks] Integrate the magnitude x² over both intervals. By symmetry this is twice the integral on [0,2].
  • [1 mark] Thus the total is 2[x³/3]₀²=16/3.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/4/2

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