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NDA2022MathematicsDefinite IntegrationActual

What is _ - / 2 ^ / 2 (e^ x x+e^ x x ) d x equal to?

Options

  1. Ae^2-1 e
  2. Be^2+1 e
  3. C1-e^2 e
  4. D0

Correct answer

A. e^2-1 e

Step-by-step solution

aligned & I= _ - / 2 ^ / 2 (e^ x x+e^ x x ) d x & = _ - / 2 ^ / 2 e^ x x d x _ - / 2 ^ / 2 e^ x x d x aligned e^ x x is odd function. _ - / 2 ^ / 2 e^ x x d x=0 Let x=t, x d x=d t when x= - 2 , t=-1 , when x= 2 , t=1 I = _ -1 ^1 e^t d t=e-e⁻¹= e^2-1 e

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