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If ∫ 0 1 e x 2 x - a d x = 0 , then the value of ∫ 0 1 e x 2 d x is equal to

Options

  1. A1 2 a e - 1
  2. Ba 2 e - 1
  3. C1 2 a e + 1
  4. Da 2 e + 1

Correct answer

A. 1 2 a e - 1

Step-by-step solution

Given, ∫ 0 1 e x 2 x - a d x = 0 ⇒ ∫ 0 1 e x 2 ⋅ x d x = a ∫ 0 1 e x 2 d x Put x 2 = t (in LHS) ⇒ x d x = d t 2 So, 1 2 ∫ 0 1 e t d t = a ∫ 0 1 e x 2 d x 1 2 e - 1 = a ∫ 0 1 e x 2 d x ∫ 0 1 e x 2 d x = 1 2 a e - 1

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