imo class 12 definite integration

Evaluate ∫₀¹ x eˣ dx.

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#IMO#Class 12#Mathematics#Definite Integration#mathematical-reasoning

Evaluate ∫₀¹ x eˣ dx.

  • A. 1
  • B. e − 1
  • C. e
  • D. 1 − e

Answer: A) 1

Explanation: Integration by parts: u = x, dv = eˣ dx. ∫₀¹ x eˣ dx = [x eˣ]₀¹ − ∫₀¹ eˣ dx = e − (e − 1) = 1.

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