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

The integral from-x to x of e^{-t} is -e^{-x}+e^x

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integral from-x to x of e^{-t}

\int_{- x}^{x} e^{- t} d t

- e^{- x} + e^{x}

Solution steps

\int_{- x}^{x} e^{- t} d t

Apply u-substitution

: \int_{x}^{- x} - e^{u} d u

= \int_{x}^{- x} - e^{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int_{x}^{- x} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - [e^{u}]_{x}^{- x}

Compute the boundaries:

e^{- x} - e^{x}

= - (e^{- x} - e^{x})

Simplify

= - e^{- x} + e^{x}

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What is the integral from-x to x of e^{-t} ?
The integral from-x to x of e^{-t} is -e^{-x}+e^x