What is the integral from-1 to 1 of e^{-2x}-1 ?

The integral from-1 to 1 of e^{-2x}-1 is (e^4-1)/(2e^2)-2

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integral from-1 to 1 of e^{-2x}-1

\int_{- 1}^{1} e^{- 2 x} - 1 d x

\frac{e ^{4} - 1}{2 e ^{2}} - 2

Decimal

1.62686 \dots

Solution steps

\int_{- 1}^{1} e^{- 2 x} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{1} e^{- 2 x} d x - \int_{- 1}^{1} 1 d x

\int_{- 1}^{1} e^{- 2 x} d x = \frac{e ^{4} - 1}{2 e ^{2}}

\int_{- 1}^{1} 1 d x = 2

= \frac{e ^{4} - 1}{2 e ^{2}} - 2

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What is the integral from-1 to 1 of e^{-2x}-1 ?
The integral from-1 to 1 of e^{-2x}-1 is (e^4-1)/(2e^2)-2