imo class 12 application of integrals

The area bounded by y = x, y = x³ and x = 0, x = 1 is:

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The area bounded by y = x, y = x³ and x = 0, x = 1 is:

  • A. 1/4 sq unit
  • B. 1/2 sq unit
  • C. 1/3 sq unit
  • D. 1/5 sq unit

Answer: A) 1/4 sq unit

Explanation: Area = ∫[0 to 1] (x − x³) dx = [x²/2 − x⁴/4]₀¹ = 1/2 − 1/4 = 1/4 sq unit.

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