integral from-2 to 2 of (|x|+x)e^{-|x|}

解答

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

2 (- \frac{3}{e ^{2}} + 1)

十进制

1.18798 \dots

求解步骤

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

拿掉绝对值

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

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

\int_{0}^{2} (x + x) e^{- x} d x = 2 (- \frac{3}{e ^{2}} + 1)

= 0 + 2 (- \frac{3}{e ^{2}} + 1)

化简

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

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