What is the integral from-5 to 10 of e^{-0.05x} ?

The integral from-5 to 10 of e^{-0.05x} is 13.54989…

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integral from-5 to 10 of e^{-0.05x}

\int_{- 5}^{10} e^{- 0.05 x} d x

13.54989 \dots

Solution steps

\int_{- 5}^{10} e^{- 0.05 x} d x

Apply u-substitution

: \int_{0.25}^{- 0.5} - \frac{1}{0.05} e^{u} d u

= \int_{0.25}^{- 0.5} - \frac{1}{0.05} e^{u} d u

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

= - \int_{- 0.5}^{0.25} - \frac{1}{0.05} e^{u} d u

Take the constant out:

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

= - (- \frac{1}{0.05} \cdot \int_{- 0.5}^{0.25} e^{u} d u)

Simplify

= - (- 20 \cdot \int_{- 0.5}^{0.25} e^{u} d u)

Use the common integral:

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

= - (- 20 [e^{u}]_{- 0.5}^{0.25})

Simplify

= 20 [e^{u}]_{- 0.5}^{0.25}

Compute the boundaries:

0.67749 \dots

= 20 \cdot 0.67749 \dots

Simplify

= 13.54989 \dots

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What is the integral from-5 to 10 of e^{-0.05x} ?
The integral from-5 to 10 of e^{-0.05x} is 13.54989…