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

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

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

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

e^{2} - e

Decimal

4.67077 \dots

Solution steps

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

Apply u-substitution

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Take the constant out:

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

= - (- \int_{1}^{2} e^{u} d u)

Use the common integral:

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

= - (- [e^{u}]_{1}^{2})

Simplify

= [e^{u}]_{1}^{2}

Compute the boundaries:

e^{2} - e

= e^{2} - e

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