What is the integral from-1 to 0 of e^{-x}-e^{2x} ?

The integral from-1 to 0 of e^{-x}-e^{2x} is e-1-(e^2-1)/(2e^2)

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integral from-1 to 0 of e^{-x}-e^{2x}

\int_{- 1}^{0} e^{- x} - e^{2 x} d x

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

Decimal

1.28594 \dots

Solution steps

\int_{- 1}^{0} e^{- x} - e^{2 x} 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}^{0} e^{- x} d x - \int_{- 1}^{0} e^{2 x} d x

\int_{- 1}^{0} e^{- x} d x = e - 1

\int_{- 1}^{0} e^{2 x} d x = \frac{e ^{2} - 1}{2 e ^{2}}

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

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What is the integral from-1 to 0 of e^{-x}-e^{2x} ?
The integral from-1 to 0 of e^{-x}-e^{2x} is e-1-(e^2-1)/(2e^2)