What is the integral from 0 to 9 of 300e^{-0.11x} ?

The integral from 0 to 9 of 300e^{-0.11x} is 1713.88175…

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integral from 0 to 9 of 300e^{-0.11x}

\int_{0}^{9} 300 e^{- 0.11 x} d x

1713.88175 \dots

Solution steps

\int_{0}^{9} 300 e^{- 0.11 x} d x

Take the constant out:

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

= 300 \cdot \int_{0}^{9} e^{- 0.11 x} d x

Apply u-substitution

: \int_{0}^{- 0.99} - \frac{1}{0.11} e^{u} d u

= 300 \cdot \int_{0}^{- 0.99} - \frac{1}{0.11} e^{u} d u

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

= 300 (- \int_{- 0.99}^{0} - \frac{1}{0.11} e^{u} d u)

Take the constant out:

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

= 300 (- (- \frac{1}{0.11} \cdot \int_{- 0.99}^{0} e^{u} d u))

Simplify

= 300 (- (- 9.09090 \dots \cdot \int_{- 0.99}^{0} e^{u} d u))

Use the common integral:

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

= 300 (- (- 9.09090 \dots [e^{u}]_{- 0.99}^{0}))

Simplify

= 2727.27272 \dots [e^{u}]_{- 0.99}^{0}

Compute the boundaries:

0.62842 \dots

= 2727.27272 \dots \cdot 0.62842 \dots

Simplify

= 1713.88175 \dots

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What is the integral from 0 to 9 of 300e^{-0.11x} ?
The integral from 0 to 9 of 300e^{-0.11x} is 1713.88175…