Calculate-2-2-x-x-e-x-dx-

Question Number 167372 by LEKOUMA last updated on 14/Mar/22

C a l c u l a t e

\int_{- 2}^{2} (∣ x ∣ + x) e^{- ∣ x ∣} d x

Answered by Mathspace last updated on 14/Mar/22

I = \int_{- 2}^{2} ∣ x ∣ e^{- ∣ x ∣} d x (\to p a i r e)

+ \int_{- 2}^{2} {x e}^{- ∣ x ∣} d x (\to i m p a i r e)

= 2 \int_{0}^{2} {x e}^{- x} d x + o

= 2 {{[- {x e}^{- x}]}_{0}^{2} - \int_{0}^{2} (- e^{- x}) d x}

= 2 {- 2 e^{- 2} + {[- e^{- x}]}_{0}^{2}}

= 2 {- 2 e^{- 2} + 1 - e^{- 2}}

= 2 {- 3 e^{- 2} + 1} = 2 - \frac{6}{e^{2}}

Commented by LEKOUMA last updated on 15/Mar/22

T h a n k s

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