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Manipal MET2020MathematicsDefinite Integration

The value of ₀^ ( / 2) (e^ x^2 ) 2 x e^ x^2 d x is

Options

  1. A1
  2. B1+ 1
  3. C1- 1
  4. D( 1)-1

Correct answer

C. 1- 1

Step-by-step solution

Given, I= ₀^ ( / 2) (e^ x^2 ) 2 x e^ x^2 d x Put e^ x^2 =t 2 x e^ x^2 d x=d t Now, lower limit, t=1 Upper limit, t=e^ / 2 = 2 I= ₁^ / 2 (t) d t=[ t]₁^ / 2 = ( 2 )- 1 I=1- 1

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