imo class 12 definite integration

Evaluate ∫[-2 to 2] (x³ cos x + |x|) dx.

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Evaluate ∫[-2 to 2] (x³ cos x + |x|) dx.

  • A. 8
  • B. 0
  • C. 4
  • D. 2

Answer: C) 4

Explanation: x³ cos x is an odd function, so its integral is 0. |x| is an even function, so ∫[-2 to 2] |x| dx = 2 ∫[0 to 2] x dx = 2[x²/2] from 0 to 2 = 4.

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